Web Analytics
Answered

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

Verified Answer :

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

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.

Related Questions