Question

Consider a function f(x) = x ^2 . A second function h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).

Answer 1

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Explanation:

Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:

The x-coordinates of f(x) and h(x) are the same, so x is unchanged.

The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.

The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.

Given the equation of f(x) = x^2, the equation of h(x) can be written as:

h(x) = -x^2 + 3

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.