Hearne ISD
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
Mathematics
Assessment
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.9 Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variety of methods
to solve them, and analyzes the solutions in terms of the situation.
2A.9(A) use the
Investigate the effects of a,
Which two
a, h, k
Holt Algebra 2
Link to ELPS
8.7
parent function to
h and k on the parent
transformations can fee
Index
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
investigate, describe,
used to obtain the graph Radical Equation
function y  x .
es/tac/chapter074/ch074a.ht
and predict the effects
Radical Function
of g(x)  x c
ml
of parameter changes
Rational Exponent
from the graph of
Verbally describe the
3H, 3D
on the graphs of
Square-Root Function
transformations (parameter
square root functions
f (x)  x if c > 0?
changes) which
Compare and contrast the
and describe
have occurred to a parent
limitations on the
graphs of y x , y a x
A. A translation to the
function.
domains and ranges;
right c units followed
y x h , and
Supporting
by a reflection across
Describe
the
effects
of
Standard
y  x k
the x-axis.
parameter changes on the
B. A translation to the
domain and range of a
College Readiness
left c units followed by
Verbally describe the effects
function.
Standard:
a reflection across the
of a, h and k on y x .
http://www.thecb.stat
x-axis.
Create
an
equation
based
e.tx.us/collegereadine
C. A translation to the
on given parameter
Describe how k effects the
ss/crs.pdf
right c units followed
changes.
range of the function.
by a reflection across
Functions A.2.a
the y-axis.
Functions B.1.b
D. A translation to the
left c units followed by
a reflection across the
y-axis.
Correct answer: A
Released EOC 2013
Q# 17
7/3/2014
Page 1
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.9(B) relate
representations of
square root functions,
such as algebraic,
tabular, graphical, and
verbal descriptions;
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Functions A.1. a
Functions A.2. a
Focus on representations of
square root functions using
algebraic equations, tables,
graphs and verbal
descriptions.
Assessment
Graph the function,
f (x) x , and
identify its domain and
range. Make a table of
values. Plot enough
ordered pairs to see the
shape of the curve.
Because the square root
of a negative is
imaginary, choose only
nonnegative values for
x.
Answer: D: [0, ∞)
R: [0, ∞)
X
0
1
4
9
7/3/2014
F(x)
0
1
2
3
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Index
Radical Equation
Radical Function
Rational Exponent
Square-Root Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
3H, 3I, 5B, 3B
Resources/
Weblinks
Holt Algebra 2
8.7
Safari Montage
Discuss how the graph,
table and equation of a
square root function are
related.
Create equations based on
written descriptions of
parameter changes.
Utilize four corners model
to represent algebraic,
tablular, graphical and
verbal.
Page 2
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.9(C) determine
the reasonable
domain and range
values of square root
functions, as well as
interpret and
determine the
reasonableness of
solutions to square
root equations and
inequalities;
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Functions B.1. b
2A.9(D) determine
solutions of square
root equations using
graphs, tables, and
algebraic methods;
Supporting
Standard
College Readiness
Standard:
http://www.thecb.state.t
x.us/collegereadiness/crs
.pdf Functions B.1. c
7/3/2014
Describe a reasonable
domain and range based on
a given square root
function.
Apply to real world
situations.
Interpret and determine the
reasonableness of solutions
to square root equations
and inequalities.
Discuss extraneous
solutions, error values in
the calculator for domain.
Assessment
1
Graph f (x)  x2 and
2
1
f (x) over the
interval 0 x 4 and
state the coordinates of
the points of
intersection.
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Index
Radical Equation
Radical Function
Rational Exponent
Square-Root Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
3I, 3B
Resources/
Weblinks
Holt Algebra 2
8.8
Safari Montage
Determine the domain and
range of a square root
function based on a real
world situation.
Answer:
Discuss the error values in
the calculator and their
association with the domain.
(2, 2)
Discuss why a solution to a
square root inequality is
reasonable or not based on
the numbers in the problem
Solve square root equations
using a variety of
methods.
What value of n makes
10 3n 7 true?
Correct answer: -13
Released EOC 2013
Q#31
Index
Radical Equation
Radical Function
Rational Exponent
Square-Root Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F
Holt Algebra 2
8.8
Solve square root equation
and higher root equations
using a variety of methods
such as reciprocal exponents
and root power.
Look at graphs and tables to
help solve.
Page 3
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.9(E) determine
solutions of square
root inequalities using
graphs and tables;
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Solve square root
inequalities using tables
and graphs. Discuss xintercept and zeros.
Assessment
Which table contains
only values in the
solution set for
y  25 x 11?
F.
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Index
Radical Equation
Radical Function
Radical Inequality
Rational Exponent
Square-Root Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F
Resources/
Weblinks
Holt Algebra 2
8.7
8.8
Solve square root
inequalities using algebra
and/or the calculator.
Functions B.1. c
G.
H.
J.
Correct answer: G
Released EOC 2013
Q# 38
7/3/2014
Page 4
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.9(F) analyze
situations modeled by
square root functions,
formulate equations
or inequalities, select
a method, and solve
problems; and
Readiness Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Create square root
equations and inequalities
modeled by a given
situation.
Use the equation/
inequality created to make
observations, conclusions
and to solve the given
problem.
Assessment
The sum of a number,
n¸ and its square root
can be represented by
the equation
y n  n . If y =
20, which of the
following is true?
A. n =16
B. n = 4
C. n =16 and n = 25
D. n = 4 and n = 5
Correct answer: A
Released EOC 2013
Q# 49
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Index
Radical Equation
Radical Function
Radical Inequality
Rational Exponent
Square-Root Function
College Readiness
Standard:
http://www.thecb.state.t
x.us/collegereadiness/crs
.pdf
Functions B.2.g
7/3/2014
Derive the square root
function by finding the
inverse of the quadratic
function and vice versa.
Discuss the domain which
makes the inverse of y=x2
a function.
Compare and constrast the
inverse graph of y = x2 and
y x.
Write the rule for the
inverse of the function.
Then state its domain
and range.
f (x) 5(x 6)2
Answer:
f 1 (x) 
x
5
D: [0, ∞)
R: [-6, ∞)
6
Holt Algebra 2
8.7
8.8
Use a four corners model to
represent square root
functions using a table, a
graph, a function rule
(equation), and a verbal
description.
Discuss extraneous
solutions.
Functions B.1. b
2A.9(G) Connect
inverses of square
root functions with
quadratic functions.
Supporting
Standard
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F, 3H, 3D
Resources/
Weblinks
Index
Radical Equation
Radical Function
Rational Exponent
Square-Root Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
3H, 3I, 1F, 1E
Holt Algebra 2
8.7 and 9.5
Using the definition of
inverse create the square
root function from a
quadratic function.
Discuss restriction on
domain to make the inverse
an actual function.
Page 5
Hearne ISD
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
Mathematics
Assessment
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.10 Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and
analyzes the solutions in terms of the situation.
2A.10(A) use
Holt Algebra 2
Discuss horizontal and
Which of the following Asymptote
Link to ELPS
quotients of
8.4
vertical asymptotes. Show
gives the equations for Continuous Function
Instructional Strategies:
polynomials to
http://ritter.tea.state.tx.us/rul 8.5
different methods for
all the vertical
Discontinuous
describe the graphs of finding and writing the
es/tac/chapter074/ch074a.ht
asymptotes of the graph
Function
rational functions,
x 4
ml
equations of asymptotes.
of f (x) 
? Extraneous Solution
predict the effects of
3I, 3D
Point of Discontinuity
(x 8)(x 5)
parameter changes,
Predict the changes in a
{Hole (in a graph) or
F. x = -4
describe limitations
Look at the rational
graph a parameter change
asymptote}
G. x = -5 and x = 8
on the domains and
functions written in standard
will create.
Rational
Equation
H. x=-2 and x = 5
1
ranges, and examine
Rational
Expression
J. x = -8 and x = 5
form ( y  ) and general
asymptotic behavior;
Compare and contrast how
Rational
Function
Correct answer: J
x
to identify the difference
Supporting
Rational Inequality
Released EOC 2013
p(x)
form ( y 
) and do the
Standard
between a vertical
Q# 42
q(x)
asymptote and a point of
discontinuity.
following:
College Readiness
Standard:
http://www.thecb.stat
Discuss how the
1. Compare how to find the
e.tx.us/collegereadine asymptotes and points of
vertical and horizontal
ss/crs.pdf
discontinuity affect the
asymptotes in the
domain and range.
different forms.
Functions B.1. b , c
2. Show the difference
Functions B.2.d
between a vertical
asymptote and a point of
discontinuity.
3. Compare the domain and
range of the parent
function and the
transformed functions.
7/3/2014
Page 6
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.10(B) analyze
various
representations of
rational functions
with respect to
problem situations;
Supporting
Standard
Model problem situations
using rational functions
and solve using graphs,
tables, verbal descriptions,
and/or equations.
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
College Readiness
Standard:
Functions B.1.b, c
7/3/2014
Michaela climbed up a
mountain at an average
speed of 3 mi/h. She
climbed down at an
average speed of 5
mi/m. What is
Michaela’s average
speed for the entire
trip? Round to the
nearest tenth.
A.
B.
C.
D.
Functions B.1. b , c
2A.10(C) determine
the reasonable
domain and range
values of rational
functions, as well as
interpret and
determine the
reasonableness of
solutions to rational
equations and
inequalities;
Supporting
Standard
Assessment
Discuss how the
asymptotes and points of
discontinuity affect the
domain and range.
Determine the
reasonableness of a
solution by looking at
graphs, equations, and
inequalities.
3.8 mi/h
4.0 mi/h
1.9 mi/h
3.9 mi/h
Answer: A
Estimate the range of
the polynomial
function.
f(x) = x3 – 4x - 5
A.
B.
C.
D.
[-5, ∞)
(-∞, ∞)
[-9, ∞)
[5, ∞)
Answer: B
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Asymptote
Combined Variation
Complex Fraction
Constant of Variation
Continuous Function
Direct Variation
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Inverse Variation
Joint Variation
Rational Equation
Rational Expression
Rational Function
Rational Inequality
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F
Asymptote
Continuous Function
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Horizontal asymptote
Points of
Discontinuity (hole in
graph or vertical
asymptote)
Rational Equation
Rational Function
Rational Inequality
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F, 1E
Resources/
Weblinks
Holt Algebra 2
8.1
8.4
8.5
Utilize ratio and proportion
word problems, variation
word problems and
similarity word problems.
Holt Algebra 2
8.5
Use the graph of a rational
to help determine its domain
and range.
Relate the asymptotes to the
domain and range.
Page 7
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.10(D) determine
the solutions of
rational equations
using graphs, tables,
and algebraic
methods;
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Algebraic C.2.a
7/3/2014
Solve rational equations
using algebraic methods,
tables, and graphs with
and without a calculator.
Assessment
What value of p makes
the equation below
true?
19
5
4 p 1
Correct answer: 1.2
Released EOC 2013
Q# 13
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Asymptote
Combined Variation
Complex Fraction
Continuous Function
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Rational Equation
Rational Expression
Rational Function
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F
Resources/
Weblinks
Holt Algebra 2
8.1
8.2
8.5
Solve by getting common
denominators, discuss
extraneous solutions and the
reason they are extraneous.
Solve by cross
multiplication.
Solve by using the
calculator and either graph
or table. (secondary)
Page 8
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.10(E) determine
solutions of rational
inequalities using
graphs and tables;
Connect solutions using
graphs and tables and
algebraic methods.
Assessment
The graph of the
function f is shown on
the grid below.
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Algebraic C.2.a
7/3/2014
Based on the graph, for
what values of x is
f(x) > 0?
F. All real numbers
greater than 0
G. All real numbers
greater than 1
H. All real numbers less
than -2 or greater than 2
J. all real numbers
greater than -2 and less
than 2
Correct answer: H
Released EOC 2013
Q# 8
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Asymptote
Continuous Function
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Rational Equation
Rational Function
Rational Inequality
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
4F
Resources/
Weblinks
Holt Algebra 2
8.5
Use sign chart and critical
numbers.
Use the graphing calculator
and graphs and tables.
(secondary)
Page 9
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.10(F) analyze a
situation modeled by
a rational function,
formulate an equation
or inequality
composed of a linear
or quadratic function,
and solve the
problem;
Readiness Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Functions C.1.a, b
7/3/2014
Create a rational equation
or inequality modeled by a
given situation.
Use the equation/inequality
created to make
observations, conclusions
and to solve the given
problem.
Assessment
The cost of printing
cookbooks is S2.09 per
book plus a one-time
setup fee of S349. All
taxes are included.
Which of the following
functions models a(x),
the average cost per
book of printing x
cookbooks?
A. a(x) 2.09x  349
x
B. a(x)  2.09x 349
x
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Asymptote
Continuous Function
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Rational Equation
Rational Function
Rational Inequality
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
3B
Resources/
Weblinks
Holt Algebra 2
8.5
Write a rational
equation/inequality given a
set of data in tabular or
graphical form.
Create a rational
equation/inequality from a
problem situation.
C. a(x)  2.09 349
2.09x
D. a(x)  2.09 x 349
2.09x
Correct answer: B
Released EOC 2013
Q# 5
Page 10
Hearne ISD
Mathematics
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
2A.10(G) use
functions to model
and make predictions
in problem situations
involving direct and
inverse variation
Supporting
Standard
College Readiness
Standard:
http://www.thecb.stat
e.tx.us/collegereadine
ss/crs.pdf
Functions B.1.c
Functions B.2. g
Describe verbally direct,
indirect and joint variation
and how they compare.
Read a real world situation
and create a variation
function to solve and
discuss reasonableness of
solution.
Assessment
The frequency of a
radio wave is inversely
proportional to the
wavelength. If a wave
250 m long has a
frequency of about
1,200 kHz, what is the
approximate length of a
wave with a frequency
of 800 kHz?
A.
B.
C.
D.
167 m
325 m
375 m
258 m
Answer: A
7/3/2014
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
Asymptote
Combined Variation
Complex Fraction
Constant of Variation
Continuous Function
Direct Variation
Discontinuous
Function
Extraneous Solution
Hole (in a graph)
Inverse Variation
Joint Variation
Rational Equation
Rational Expression
Rational Function
Rational Inequality
Link to ELPS
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
es/tac/chapter074/ch074a.ht
ml
2F
Resources/
Weblinks
Holt Algebra 2
8.1
Differentiate between direct,
indirect and joint variation.
Find the constant of
variation and use it to help
solve the problem asked.
(Real World )
Connect direct variation to
linear functions and inverse
variation to rational
functions.
Page 11
Hearne ISD
Course: Algebra II
Unit: Radical and Rational Functions
TEKS
Guiding Questions/
Specificity
Mathematics
Assessment
Designated Six Weeks: 5th
Days to teach: 28 days
Vocabulary
Instructional
Strategies
2A.4 Algebra and geometry. The student connects algebraic and geometric representations of functions.
2A.4(B) extend
Describe changes in the
Which equation might a ,h, k
Link to ELPS
parent functions with
graph of f(x) when
have the graph shown Asymptote
Instructional Strategies:
http://ritter.tea.state.tx.us/rul
parameters such as a
transformed as follows: f
below?
Continuous Function
es/tac/chapter074/ch074a.ht
in f (x) = a/x and
(x – h), f(x) + k, af(x), and
Discontinuous
ml
describe the effects of af(x – h) + k, f(-x), -f(x),
Function
3H, 1E, 3I
the parameter changes (stretches (narrows),
Extraneous Solution
on the graph of parent shrinks (widens), translates
Hole (in a graph)
Make and describe a chart
functions; and
right/let or up/down and
Rational Equation
of the parent functions
reflection).
Rational Function
Readiness Standard
including linear, quadratic,
Rational Inequality
3
exponential and logarithmic
Describe verbally the
College Readiness
A. y 
functions. Have students
changes in the graph when
Standard:
x 2
investigate and describe
http://www.thecb.stat
each parameter changes.
x
B. y 
e.tx.us/collegereadine
transformations. Practice
x 2
ss/crs.pdf
with transformations
3
charades, filling out a chart
C.
y

Functions B.2.c
where student graph and
x 2
describe all changes.
x
D. y 
x 2
Resources/
Weblinks
Holt Algebra 2
9.3
8.7
Answer: C
7/3/2014
Page 12