Question

Which exponential function has an x-intercept?

A. f(x) = 100x−5 − 1

B. f(x) = 3x−4 + 2

C. f(x) = 7x−1 + 1

D. f(x) = -8x+1 − 3

Answer 1

It would be C since it would be f(x) = 7x

Answer 2

Answer:

Option A - x-intercept is at (5,0)

Step-by-step explanation:

Given : Exponential Functions

To find : Which exponential function has an x-intercept?

Solution :

x-intercept is the value at which the value of y=0.

To find the x-intercept we have to substitute y=0 or f(x)=0           

A. $f(x)=100^{x-5}-1$      

x-intercept at f(x)=0    

$0=100^{x-5}-1$    

$100^{x-5}=1$    

Taking log both side,

${x-5}\log 100=\log 1$  

${x-5}(2)=0$    

$x-5=0$    

$x=5$    

Therefore, the x-intercept of the given function is (5,0).

B. $f(x)=3^{x-4}+2$      

x-intercept at f(x)=0    

$0=3^{x-4}+2$    

$3^{x-4}=-2$    

Taking log both side,

${x-4}\log 3=\log (-2)$  

Since, log (-2) is not defined.

Therefore, the x-intercept of the given function is none.

C. $f(x)=7^{x-1}+1$      

x-intercept at f(x)=0    

$0=7^{x-1}+1$    

$7^{x-1}=-1$    

Taking log both side,

${x-1}\log 7=\log (-1)$  

Since, log (-1) is not defined.

Therefore, the x-intercept of the given function is none.

D. $f(x)=-8^{x+1}-3$      

x-intercept at f(x)=0    

$0=-8^{x+1}-3$    

$-8^{x+1}=3$    

Taking log both side,

${x+1}\log (-8)=\log (3)$  

Since, log (-8) is not defined.

Therefore, the x-intercept of the given function is none.

Hence, Option A has only x-intercept.