Content Area
Standard
Strand
Content Statement
Math
4.HS High School
F-LE Functions – Linear, Quadratic, & Exponential Models
CPI#
Cumulative Progress Indicator
(CPI)
ACSSSD
Objectives
Construct and compare linear, quadratic, and exponential models and solve problems.
4.HS. FLE.1
a.
Distinguish between situations that can be modeled with linear functions
and with exponential functions.
Prove that linear functions grow by
equal differences over equal intervals,
and that exponential functions grow
by equal factors over equal intervals.
1. Refer to the ACSSSD
Objectives of 4.HS.F-IF.1 for
prerequisite skills needed to
complete this CPI.
2. Demonstrate the ability to
use the vertical line test to
determine if a relation is a
function meaning that if a
vertical line can be drawn so
that it intersects the graph of
a relation more than once,
the relation is not a function.
3. Recognize that in
exponential expressions the
exponent is the variable, the
base is a fixed number and is
also referred to as the
multiplier.
4. Recognize that exponential
functions are written in the
form f(x)=bx where the base
b is fixed and the exponent is
the variable, b is any positive
real number other than 1 and
the exponent is any real
number.
5. Recognize that when the
base in an exponential
function is greater than 1, the
function represents
exponential growth.
6. Recognize that when the
base in an exponential
function is greater than 0, but
less than 1, the function
represents exponential decay.
7. Demonstrate the ability to
solve linear functions and
exponential functions.
b.
Recognize situations in which one
1. Refer to the ACSSSD
quantity changes at a constant rate per
Objectives for 4.HS.ACED.2 and 4.HS.A-REI.10
unit interval relative to another.
for the prerequisite skills
needed to complete this CPI.
c.
Recognize situations in which a
quantity grows or decays by a
constant percent rate per unit interval
relative to another.
1. Demonstrate the ability to
write an exponential
expression that demonstrates
growth over time by adding
the percent of growth to 100
to find the multiplier.
2. Demonstrate an
understanding that rate of
decay can be seen as
negative growth rate.
3. Demonstrate the ability to
write and an exponential
expression that demonstrates
decay over time by
subtracting the percent of
growth from 100 to find the
multiplier.
4. Recognize that the exponent
represents the period of time
of growth or decay.
4.HS. FLE.2
Construct linear and exponential
functions, including arithmetic and
geometric sequences, given a graph, a
description of a relationship, or two
input-output pairs (include reading
these from a table).
1. Refer to ACSSSD Objectives
for 4.HS.A-SSE.4, 4.HS.ACED.2, 4.HS.A-REI.6,
4.HS.F-IF.2 and 4.HS.F-IF.9
for the prerequisite skills
needed to complete this CPI.
4.HS. FLE.3
Observe using graphs and tables that
a quantity increasing exponentially
eventually exceeds a quantity
increasing linearly, quadratically, or
(more generally) as a polynomial
function.
1. Refer to ACSSSD Objectives
for 4.HS.F-IF.7c, 4.HS.FIF.7d, 4.HS.A-SSE.3c for the
prerequisite skills needed to
complete this CPI.
2. Recognize that growth of
exponential functions
eventually overtakes the
growth of other functions
because it doubles
continuously over time.
Interpret expressions for functions in terms of the situation they model.
4.HS. FLE.5
Interpret the parameters in a linear or
exponential function in terms of a
context.
1. Refer to ACSSSD Objectives
for 4.HS.F-IF.1 and 4.HS. FLE.1a for the prerequisite
skills needed to complete this
CPI.
2. Demonstrate the ability to
determine which solutions to
real world problems can be
found using linear functions
and which can be found
using exponential functions.