Chapter 8, Problem 1VR

Complete each statement with the correct term from the column on the right. Some of the choices may not be used.

exponential

logarithmic

common

natural

composition

compound

inverse

double time

half-life

base

exponent

The function given by $f\left(x\right)=6^x$ is an example of a(n) _________function. [8.1a]

To determine

To fill: The blank provided in the statement, “The function given by $f\left(x\right)=6^x$ is an example of a(n) ______ function”, from the provided choices.

Answer to Problem 1VR

Solution:

The function given by $f\left(x\right)=6^x$ is an example of an exponential function.

Explanation of Solution

Given Information:

The provided function is $f\left(x\right)=6^x$. The provided choices are,

Exponential

Logarithmic

Common

Natural

Composition

Compound

Inverse

Double Time

Half-life

Base

Exponent

Consider the function, $f\left(x\right)=6^x$

If a function is in the form of $f\left(x\right)=a^x$, where a is a positive constant $a\ne 1$ then it is said to be an exponential function.

Compare the function $f\left(x\right)=6^x$ and $f\left(x\right)=a^x$.

The value of base $a$ is $6$. So, it follows $a\ne 1$.

So, the function $f\left(x\right)=6^x$ is an exponential function.

Therefore, the correct fill for the blank is exponential.