Question

The function f(x) = 5 * (1/5) ^ x reflected over the yaxis. Which equations represent the reflected function? Select two options please I really need help

Answer 1

f(x) = 5(1/5) ⁻ˣ

f(x) = 5(5)ˣ

Answer 2

The following two equations represent the reflected function:

f(x) = 5(1/5) ⁻ˣ

f(x) = 5(5)ˣ

Explanation:

Following are two basic concepts of reflection a point or a function over an axis:

• If a point or a function is reflected across x-axis, the x component remains the same while the y component changes its sign.
• If a point or a function is reflected across y-axis, the y component remain the same while the x component changes its sign.

In this question, the function is given:

f(x) = 5(1/5)ˣ

As the function is reflected over y-axis, it follows the second concept. The x component will becomes negative.

So the equation of reflected function is:

f(x) = 5(1/5) ⁻ˣ

We know that that fraction with a negative power can also be written as a reciprocal of the same fraction with a positive power.

(1/5)⁻ˣ = 5ˣ

So equation of reflected function can also be written as:

f(x) = 5(5)ˣ