Chapter 8.1, Problem 34HP

a.

To determine

To find: Whether the given statement is sometimes, always, or never true.

Explanation of Solution

Given information:

The given statement is, “An exponential function of the form $y=a{b}^{x-h}+k$ has a y -intercept”.

Consider the following graph of the function is,

  

Thus, the statement “the exponential function of the form $y=a{b}^{x-h}+k$ has a y -intercept” is always true.

b

To determine

To find: Whether the given statement is sometimes, always, or never true.

Explanation of Solution

Given information:

The given statement is, “An exponential function of the form $y=a{b}^{x-h}+k$ has a x -intercept”.

Consider the following graph of the function is,

  

At $y=0$ , function has x -intercept.

Thus, the statement “the exponential function of the form $y=a{b}^{x-h}+k$ has a y -intercept” is sometime true.

c

To determine

To find: Whether the given statement is sometimes, always, or never true.

Explanation of Solution

Given information:

The given statement is, “The function $f\left(x\right)={\left|b\right|}^x$ is an exponential growth function if $b$ is an integer”.

The given function is mod function so for any integer value of b , the function is an exponential growth function.

Thus, the statement “the exponential function of the form $y=a{b}^{x-h}+k$ has a y -intercept” is always true.