Topics
5. Linear and Exponential Models
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United States of America
Grades 9-12

5.06 Comparing linear and exponential functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the two functions shown in the graph below:

Loading Graph...

a

State the negative interval(s) of function $f$f, using inequality notation.

b

State the negative interval(s) of function $g$g, using inequality notation.

c

Fill in the blanks to describe the end behavior of function $f$f:

As $x\to\infty$x→∞, $f\left(x\right)\to$f(x)→$\editable{}$

As $x\to-\infty$x→−∞, $f\left(x\right)\to$f(x)→$\editable{}$

d

Fill in the blanks to describe the end behavior of function $g$g:

As $x\to\infty$x→∞, $g\left(x\right)\to$g(x)→$\editable{}$

As $x\to-\infty$x→−∞, $g\left(x\right)\to$g(x)→$\editable{}$

e

Determine whether each function is linear or nonlinear.

$f$f is a linear function, while $g$g is a nonlinear function

A

$f$f is a nonlinear function, while $g$g is a linear function

B

Both functions are linear

C

Both functions are nonlinear

D
Easy
2min

Consider the two functions shown in the graph below:

Easy
2min

Function $f$f is given by the equation $f\left(x\right)=2x-0.4$f(x)=2x−0.4. Function $g$g is shown in the graph below.

Medium
2min

Function $f$f is given by the equation $f\left(x\right)=-4$f(x)=−4. Function $g$g is shown in the graph below.

Medium
2min
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Outcomes

A.REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately.

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.B.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.

F.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F.LE.A.1.A

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

F.LE.A.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.

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