Algebra 1
Georgia Milestones Review
Unit 5: Comparing and Contrasting Functions
A family invested $2,000 into an account that pays 2% interest compounded annually. In the functions below, x represents time in
years and y represents the total amount in the account after x years.
F.LE.1
F.LE.1a
Distinguish between
situations that can be
modeled with linear
functions and with
exponential functions.
Show that linear
functions grow by equal
differences over equal
intervals and that
exponential functions
grow by equal factors
over equal intervals. (This
can be shown by
algebraic proof, with a
table showing
differences, or by
calculating average rates
of change over equal
intervals).
𝑦 = 40𝑥 + 2,000
𝑦 = 2000(1.02)𝑥
Use the function that models the situation correctly. To the nearest dollar, how much money is in the family account after 5 years?
A) $2.081
B) $2,200
C) $2, 208
D) $10,200
The following tables show the values of different functions at various values of x. Identify each function as linear, exponential, or
neither.
The table represents the world population (in billions) and the year it was reached. Based on the data in the table below, would a
linear function be an appropriate model? Explain why or why not.
F.LE.1b
Recognize situations in
which one quantity
changes at a constant
rate per unit interval
relative to another.
1804
1927
1960
1974
1987
1999
2012
1
2
3
4
5
6
7
For each or the scenarios below, decide whether or not the situation can be modeled by an exponential function.
a. From 1910 until 2010 the growth rate of the United States has been steady at about 1.5% per year. The population in 1910 was
about 92,000,000.
F.LE.1c
Recognize situations ina.
which a quantity grows
or decays by a constantb.
percent rate per unit
interval relative to
another.
b. The circumference of a circle as a function of the radius.
c. According to an old legend, an Indian King played a game of chess with a traveling sage on a beautiful, hand-made chessboard.
The sage requested, as reward for winning the game, one grain of rice for the first square, two grains for the second, four grains
for the third, and so on for the whole chess board. How many grains of rice would the sage win for the nth square?
c.
d.
d. The volume of a cube as a function of its side length.
e.
F.LE.2
Construct linear and
exponential functions,
including arithmetic and
geometric sequences,
given a graph, a
description of a
relationship, or two
input-output pairs
A certain car depreciates at a rate of 15% per year. If the purchase price of the car is $26,000, what will be the value of the car
after 6 years?
A) $3,900
B) $9,806
C) $22,100
D) $22,609
Algebra 1
(include reading these
from a table).
Georgia Milestones Review
Which rule applies to the table below?
A) 𝑦 = 9 ∙ 3𝑥
B) 𝑦 = 3 ∙ 9𝑥
1 𝑥
C) 𝑦 = 3 ∙ ( )
9
1 𝑥
D) 𝑦 = 9 ∙ ( )
3
The first four terms of two different sequences are shown below. Sequence 𝐴 is given in the table, and sequence 𝐵 is graphed as a
set of ordered pairs.
F.LE.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.
F.LE.5
Interpret the parameters
in a linear (f(x) = mx + b)
and exponential ( f(x) = a
dx ) function in terms of
context. (In the functions
above, “m” and “b” are
the parameters of the
linear function, and “a”
and “d” are the
parameters of the
exponential
function.) In context,
students should describe
what these parameters
mean in terms of change
and starting value.
Which sequence will be the first to exceed 500? How do you know?
The number of bacteria present in a laboratory sample after t days can be represented by = 500(2𝑡 ) . What is the initial number
of bacteria present in this sample?
A)
B)
C)
D)
250
500
750
1000
The function y = 6 + 1.25x can be used to find the cost of joining an online music club and buying x songs from the website. Based
on this information, which statement about the graph of this situation is true?
A) The y-intercept of the graph represents the cost of each song.
B) The y-intercept of the graph represents the cost of joining the music club.
C) The slope of the graph represents the total number of songs bought by members of the club.
D) The slope of the graph represents the number of songs each member buys when visiting the website.
The graph of 𝑦 = 3𝑥 − 2 is translated up 5 units. What is the equation of the new graph?
F.BF.3
Identify the effect on the
graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and
f(x + k) for specific values
of k(both positive and
negative); find the value
of k given the graphs.
Experiment with cases
and illustrate an
explanation of the effects
on the graph using
technology. Include
recognizing even and odd
functions from their
graphs and algebraic
expressions for them.
A) 𝑦 = 8𝑥 − 2
B) 𝑦 = 3𝑥 + 3
C) 𝑦 = 3𝑥 − 7
D) 𝑦 = 3𝑥 + 5
If c = −5, how does the graph of 𝑦 = 𝑥 2 + 2𝑐 compare to the graph of = 𝑥 2 + 𝑐 ?
A) The graph of 𝑦 = 𝑥 2 + 2𝑐 is below the graph of 𝑦 = 𝑥 2 + 𝑐.
B) The graph of 𝑦 = 𝑥 2 + 2𝑐 is above the graph of 𝑦 = 𝑥 2 + 𝑐.
C) The graph of 𝑦 = 𝑥 2 + 2𝑐 is narrower than the graph of 𝑦 = 𝑥 2 + 𝑐.
D) The graph of 𝑦 = 𝑥 2 + 2𝑐 is wider than the graph of 𝑦 = 𝑥 2 + 𝑐.
Algebra 1
F.IF.1
Understand that a
function from one set
(the input, called the
domain) to another set
(the output, called the
range) assigns to each
element of the domain
exactly one element of
the range, i.e. each input
value maps to exactly
one output value. If f is a
function, x is the input
(an element of the
domain), and f(x) is the
output (an element of
the range). Graphically,
the graph is y = f(x).
Georgia Milestones Review
Which of the following mappings best represents the function f(x) = −x2 + 3?
A)
B)
C)
D)
Jamie has a plan to save money for a trip. Today, she put 5 pennies in a jar. Tomorrow, she will put the initial amount plus another
5 pennies. Each day she will put 5 pennies more than she put into the jar the day before, as shown in the table.
Let 𝑓(𝑑) represent the amount of pennies she puts into the jar on day d. What does 𝑓(10) = 55 mean?
A) Jamie will put 10 pennies in the jar on day 55.
F.IF.2
Use function notation,
evaluate functions for
inputs in their domains,
and interpret statements
that use function
notation in terms of a
context.
B) Jamie will put 55 pennies in the jar on day 10.
C) Jamie will have 10 pennies in the jar on day 55.
D) Jamie will have 55 pennies in the jar on day 10.
Algebra 1
Georgia Milestones Review
The table below shows ordered pairs of a linear function.
F.IF.4
Using tables, graphs, and
verbal descriptions,
interpret the key
characteristics of a
function which models
the relationship between
two quantities. Sketch
a graph showing key
features including:
intercepts; interval
where the function is
increasing, decreasing,
positive, or negative;
relative maximums and
minimums; symmetries;
end behavior
What are the x- and y-intercepts for the graph of this linear function?
A) x-intercept: (−6, 0)
y-intercept: (0, 9)
B) x-intercept: (0, −6)
y-intercept: (9, 0)
C) x-intercept: (0, 9)
y-intercept: (−6, 0)
D) x-intercept: (9, 0)
y-intercept: (0, −6)
F.IF.5
Relate the domain of a
function to its graph and,
where applicable, to the
quantitative relationship
it describes. For example,
if the function h(n) gives
the number of personhours it takes to
assemble n engines in a
factory, then the positive
integers would be an
appropriate domain for
the function.
Given the functions g(x), f(x), and h(x) shown below:
F.IF.6
Calculate and interpret
the average rate of
change of a function
(presented symbolically
or as a table) over a
specified interval.
Estimate the rate of
change from a graph.
The correct list of functions ordered from greatest to least by average rate of change over the interval 0 ≤ 𝑥 ≤ 3 is
A)
B)
C)
D)
f(x), g(x), h(x)
h(x), g(x), f(x)
g(x), f(x), h(x)
h(x), f(x), g(x)
Algebra 1
Georgia Milestones Review
On the coordinate plane provided, graph the line with equation 5𝑦 − 3𝑥 = −15. Identify the x- and y-intercepts.
F.IF.7
Graph functions
expressed algebraically
and show key features of
the graph both by hand
and by using technology.
A portion of the graph of a quadratic function f(x) is shown in the xy-plane. Selected values of a linear function g(x) are shown in
the table.
Use a comparison symbol ( =, >, <, >, < ) to indicate the relationship between the first and second quantity.
F.IF.9
Compare properties of
two functions each
represented in a
different way
(algebraically,
graphically, numerically
in tables, or by verbal
descriptions). For
example, given a graph of
one function and an
algebraic expression for
another, say which has
the larger maximum.
Compare the following three functions.
i. A function 𝑓 is represented by the graph below
ii. A function 𝑔 is represented by the following equation.
𝑔(𝑥) = (𝑥 − 6)2 – 36
iii. A linear function ℎ is represented by the following table
For each of the following, evaluate the three expressions given, and identify which expression has the largest value and which has
the smallest value. Show your work.
a. 𝑓(0), 𝑔(0), ℎ(0)
b. 𝑓(1000), 𝑔(1000), ℎ(1000)
Algebra 1
Georgia Milestones Review