Question

Which exponential function does not have an x-intercept?

f(x) = 5x – 5 – 1
f(x) = 5x – 5 – 5
f(x) = -5x – 5 + 5
f(x) = -5x – 5 – 1

Answer 1

The correct option is 4.

Explanation:

Find the x-intercept of each function.

1.
`f(x)=5^((x-5))-1`

Substitute f(x)=0, to find the x-intercept.

`0=5^((x-5))-1`

`1=5^((x-5))`

`5^0=5^((x-5))`

On comparing the powers, we get

`0=x-5`

`x=5`

The x-intercept of this function is 5.

2.
`f(x)=5^((x-5))-5`

Substitute f(x)=0, to find the x-intercept.

`0=5^((x-5))-5`

`5=5^((x-5))`

`5^1=5^((x-5))`

On comparing the powers, we get

`1=x-5`

`x=6`

The x-intercept of this function is 6.

3.
`f(x)=-5^((x-5))+5`

Substitute f(x)=0, to find the x-intercept.

`0=-5^((x-5))+5`

`5^((x-5))=5`

`5^((x-5))=5^1`

On comparing the powers, we get

`x-5=1`

`x=6`

The x-intercept of this function is 6.

4.
`f(x)=-5^((x-5))-1`

Substitute f(x)=0, to find the x-intercept.

`0=-5^((x-5))-1`

`1=-5^((x-5))`

`-1=5^((x-5))`

This statement is not true for any value of x. Therefore this function has not x-intercept.

Option 4 is correct.