Question

Which exponential function has an x-intercept

A) f(x)=100^x-5 -1
B) f(x)=3^x-4 -2
C) f(x)=7^x-1 +1
D) f(x)=8^x+1 -3

Answer 1

Option B) f(x) = 3^(x-4) - 2 is the exponential function that has an x-intercept.

Step-by-step explanation:

To find the exponential function that has an x-intercept, we need to set the function equal to zero and solve for x. Let's go through the options:

Option A: f(x) = 100^(x-5) - 1. If we set this equal to zero, we get 100^(x-5) - 1 = 0. Solving for x, we find x = 5. So the x-intercept is 5, but this does not match the given criteria.

Option B: f(x) = 3^(x-4) - 2. Setting this equal to zero, we get 3^(x-4) - 2 = 0. Solving for x, we find x = 4. So the x-intercept is 4, which matches the given criteria.

Option C: f(x) = 7^(x-1) + 1. Setting this equal to zero, we get 7^(x-1) + 1 = 0. But raising any number to a power greater than or equal to zero results in a positive value, so this option does not have an x-intercept.

Option D: f(x) = 8^(x+1) - 3. Setting this equal to zero, we get 8^(x+1) - 3 = 0. Solving for x, we find x = -1. So the x-intercept is -1, but this does not match the given criteria.

Therefore, the correct option is B) f(x) = 3^(x-4) - 2.

Answer 2

I suppose you thought the following:

A) f(x) = 100^(x-5) - 1
B) f(x) = 3^(x-4) - 2
C) f(x) = 7^(x-1) + 1
D) f(x) = 8^(x+1) - 3

In that case the correct answers are A), B) and D)

Good luck!!!