Introduction (P)
Tables (1.2)
Rule Use parentheses ( and ) to
maintain order of operations
with fractions and exponents.
Note Use the 2nd ANS key to recall
the result of the last operation.
Note Use the 2nd ENTRY key to recall
the last set of keystrokes.
Functions and Models (1.1)
Def’n A function describes a relationship
between inputs and an output.
Def’n A model uses a function to describe
a real situation or process.
Note Functions can be represented using
formulas, tables, or graphs.
Formulas (1.1)
Def’n A formula describes a function
using numbers, letters, and symbols.
Def’n When equation notation is used,
the output variable is represented
by only a letter.
Def’n When function notation is used,
the output variable makes reference
to the input variable(s).
Def’n A table describes a function using
columns of input and output values.
Rule When estimating an output value
for an input value halfway between
two table values, average the two
corresponding output values.
Average Rate of Change (1.2)
Def’n The average rate of change of a
function is the difference in the
output variable divided by the
difference in the input variable.
AROC 
 output
 input
Def’n A limiting value exists whenever
output values level off while input
values continue to rise.
Graphs (1.3)
Def’n A graph describes a function using a
two-dimensional picture with labels
and headings.
Def’n A graph is increasing if it rises from
left to right, and decreasing if it falls
from left to right.
Creating Tables in the TI-83 (2.1)
 Type an equation into Y1 using
the Y= key.
 Select the table features using
the 2nd TBLSET key.
 View the table using the
2nd TABLE key.
Def’n The minimum is the lowest output
value, and the maximum is the
highest output value.
Features of TI-83 Tables (2.1)
Concavity (1.3)
Rule Find limiting values by setting
Tbl  1000 .
Def’n A graph is concave up if its ends are
are bent upward, and concave down
if its ends are bent downward.
Def’n An inflection point occurs where
concavity changes from up to down
or from down to up.
Rule Find input values, inflection
points, minimum values, or
maximum values by setting
Tbl  0.01.
Creating Graphs on the TI-83 (2.2)
 Type an equation into Y1 using
the Y= key.
 Select the viewing area for the
graph using the WINDOW key.
 View the graph using the GRAPH key.
Features of TI-83 Graphs (2.2, 2.4, 2.6)
Rule Calculate output values using the
2nd CALC value feature.
Slope (3.1)
Def’n The slope m of a line is the ratio of
the vertical change between any two
points on the line to the horizontal
change between the same two points:
m
y rise

x run
Note The slope formula can be rearranged
to solve for y or x as follows:
y  m  x
x 
y
m
Rule Find limiting values using the
TRACE key.
Linear Functions (3.2, 3.3)
Rule Calculate input values using the
2nd CALC intersect feature.
Def’n A linear function is a function with
a constant rate of change.
Rule Calculate inflection points using the
2nd CALC dy/dx feature
Rule A linear function can be written as
y  mx  b , where m is the AROC
and b is the initial value.
Rule Locate minimum values using the
2nd CALC minimum feature.
Rule Locate maximum values using the
2nd CALC maximum feature.
Finding Linear Equations (3.2, 3.3)
Rule If the slope m and one data point (x , y )
are given, plug the values into the
equation y  mx  b and solve for b.
Rule If two data points are given, first
calculate the slope m, then plug in
and solve for b as above.
Modeling Nearly Linear Data (3.4)
Exponential Functions (4.1)
Rule Model data that are nearly linear
using a method called least-squares
linear regression.
Def’n An exponential function is
a function with a constant
percentage rate of change.
 Type the input values into L1 and
the output values into L2 using the
STAT EDIT feature.
 Calculate the line of best fit using
the STAT CALC LinReg(axb)
feature.
 View the graph of the points and the
line using the 2nd STATPLOT key.
Rule An exponential function can
be written as y  a  b x , where
a is the initial value and b is
the growth or decay factor.
Rule A factor greater than one indicates
growth, while a factor less than one
indicates decay.
Def’n The growth or decay rate r is given
by: r  b  1, and the growth or decay
factor b is given by: b  r  1 .
Solving Linear Systems (3.5)
Rule Solve linear systems by:
(1) writing two equations from words,
(2) solving both equations for the
same variable,
(3) typing the equations into Y1
and Y2, and
(4) locating the intersection of the
graphs of the equations using the
2nd CALC intersect feature.
Unit Conversion for Factors and Rates (4.2)
Rule The growth or decay factor for a
time period of k units is bk, while
a growth or decay rate for a time
period of k units cannot be found
directly.
Rule Exponential growth can be shown
using by a doubling time, and
exponential decay can be shown
using a half-life.
Finding Exponential Equations (4.1-4.3)
Power Functions (5.2)
Rule If the growth or decay factor b and
and one data point (x , y ) are given,
plug the values into the equation
y  a  b x and solve for a.
Def’n A power function is a function with
an output that is proportional to a
power of the input.
Rule If a doubling time or half-life x is given,
plug the values into the equation
y  a  b x and solve for b.
Rule If two adjacent data points are given,
first calculate the factor b  y 2 y1 ,
then plug in and solve for a as above.
Exponential Regression (4.4)
Rule Model data that are nearly exponential
using exponential regression.
Rule A power function can be written as
y  a  x b , where a is a constant and
b is the power.
Rule If the input is multiplied by k, then
the output is multiplied by kb.
Power (5.2)
Rule If b  1, the function is
increasing and concave up.
If 0  b  1, the function is
increasing and concave down.
If b  0 , the function is
decreasing and concave up.
Finding Power Equations (5.2)
Rule If the power b and one data point
(x , y ) are given, plug the values into
the equation y  a  x b and solve for a.
Power Regression (5.3)
Rule Model data that are nearly power
using power regression.
Logistic Functions (5.1)
Quadratic Functions (5.5)
Def’n A logistic function is a function
that modifies exponential growth
by limiting the output value.
Rule A quadratic function can be written
as y  ax 2  bx  c , where c is the
initial value.
Rule A logistic function can be written
C
as y 
, where C is the
1  a  e Rx
Rule The graph of a quadratic function is
a parabola with either a maximum
or minimum value.
carrying capacity,
C
1a
is the
initial value, and R is the intrinsic
growth rate.
Rule A logistic function has an inflection
point located where y 
C
2
.
Rule Model data that are nearly quadratic
using quadratic regression.
Cubic Functions (5.5)
Rule A cubic function can be written
as y  ax 3  bx 2  cx  d .
Rule The corresponding exponential
growth factor is given by: b  e R ,
and the intrinsic growth rate is
given by: R  ln b .
Rule The graph of a cubic function has an
inflection point and changes direction
twice.
Rule Model data that are nearly logistic
using logistic regression.
Rule Model data that are nearly cubtic
using cubic regression.
Rational Functions (5.5)
Rule A rational function can be written as
a ratio of two polynomial functions.
Rule A rational function may have a limiting
value, vertical asymptotes, both, or
neither.