Question

Which is the range of the function f(x) =One-seventh(9)x?

a: all real numbers
b: all real numbers less than 0
c:all real numbers greater than 0
d: all real numbers less than or equal to 0

Answer 1

Answer: all real numbers greater than 0

Explanation:

Range is the set of y values for which the function is defined using a graphing tool

The domain is the interval ----> (-∞,∞) All real numbers

For all positive and negative values for x the value of y is always positive

The range is the interval ---->(0,∞)

All real numbers greater than 0

Answer 2

Option c: all real numbers greater than 0

Explanation:

we have

`f(x)=(1)/(7)(9^(x))`

This is a exponential function of the form

`f(x)=a(b^(x))`

where

a is the initial value (y-intercept)

b is the base

r is the rate

b=(1+r)

In this problem we have

a=1/7

b=9

r=b-1 ----> r=9-1=8 -----> r=800%

using a graphing tool

see the attached figure

The domain is the interval ------> (-∞,∞)

The domain is all real numbers

The range is the interval ---------> (0,∞)

The range is all real numbers greater than zero