Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Complete the following questions to practice the skills you have learned in this lesson.

Functions $a, b, c, d, e$ , and $f$ are given below. Which functions are linear? Select the three answers that apply.

$a(x)=3x$
$b(x)=3^x$
$c(x)=x^3$
$d(x)=9+3x$
$e(x)=9 \cdot 3^x$
$f(x)=9 \cdot 3x$

Functions $a, b, c, d, e$ , and $f$ are given below. Which functions are exponential? Select the two answers that apply.

$a(x)=3x$
$b(x)=3^x$
$c(x)=x^3$
$d(x)=9+3x$
$e(x)=9\cdot 3^x$
$f(x)=9\cdot 3x$

Here are 4 equations defining 4 different functions, a , b , c , and d . List them in order of increasing rate of change. That is, start with the one that grows the slowest and end with the one that grows the quickest.
- $a(x)=5x+3$
- $b(x)=3x+5$
- $c(x)=x+4$
- $d(x)=1+4x$

Option 4: $c(x)$ , $b(x)$ , $d(x)$ , $a(x)$
Option 3: $a(x)$ , $d(x)$ , $b(x)$ , $a(x)$
Option 2: $d(x)$ , $c(x)$ , $b(x)$ , $a(x)$
Option 1: $a(x)$ , $b(x)$ , $c(x)$ , $d(x)$

Use the given information for problems 4 – 6. Technology is required. Function $f$ is defined by $f(x)=3x+5$ , and function $g$ is defined by $g(x)=(1.1)^x$ .

	$f(x)$	$g(x)$
1
5
10
20

Table 5.14.0

Which values will complete the table for $f(x)$ ?

8, 15, 30, 60
3, 15, 30, 60
8, 20, 35, 65
8, 11, 14, 17

Which of the following sets of values will complete the table for $g(x)$ ?

1.1, 1.21, 1.33, 1.46
1.1, 1.6, 2.59, 6.73
1.1, 5.5, 10.10, 20.20
8, 20, 35, 65

1. ________ is a linear function.

neither
g(x)
f(x)

________ is an exponential function.

neither
g(x)
f(x)

Functions $m$ and $n$ are given by $m(x)=(1.05)^x$ and $n(x)=\frac{5}{8}x$ . As $x$ increases from 0, __________ reaches 30 first.

neither
n(x)
m(x)

Functions $m$ and $n$ are given by $m(x)=(1.05)^x$ and $n(x)=\frac{5}{8}x$ . As $x$ increases from 0, __________ reaches 100 first.

neither
n(x)
m(x)

The functions $f$ and $g$ are defined by $f(x)=8x+33$ and $g(x)=2 \cdot(1.2)^x$ . Which function eventually grows faster, $f$ or $g$ ? Explain how you know.

$g(x)$ grows faster because it is an exponential function.
$g(x)$ grows faster because it is a linear function.
$f(x)$ grows faster because 33 is greater than 2.
$f(x)$ grows faster because 8 is greater than 1.2.

A line segment of length $l$ is scaled by a factor of 1.5 to produce a segment with length $m$ . The new segment is then scaled by a factor of 1.5 to give a segment of length $n$ .

What scale factor takes the segment of length $l$ to the segment of length $n$ ?

5.14.5 Practice