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

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

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.