Question

Which exponential function does not have an x-intercept?

Answer 1

   f(x) = -5x – 5 + 5    Hope this helps!

Answer 2

Answer:

The correct option is 4.

Step-by-step 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.