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Alexxandr [17]
3 years ago
9

Which exponential function has an x-intercept?

Mathematics
2 answers:
weeeeeb [17]3 years ago
8 0

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.

Rzqust [24]3 years ago
6 0
It would be C since it would be f(x) = 7x
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