Question

"3. Given f(x)= 1 / 3 x-8, answer the following questions.

a. What would f(x) change to if the function is reflected across the x-axis?
b. What would the new equation (in a) change to if it is translated up 17 units?"

Answer 1

To reflect the given function across the x-axis, change the sign of the y-values. To translate the reflected equation up 17 units, add 17 to the equation.

Step-by-step explanation:

To reflect a function across the x-axis, we change the sign of the y-values. In the given function f(x) = 1 / 3x - 8, reflecting across the x-axis would result in f(x) = -1 / 3x - 8. The equation has the same form as the original with a negative sign in front of the fraction.

To translate the reflected equation up 17 units, we add 17 to the equation. Therefore, the new equation (after reflection and translation) would be f(x) = -1 / 3x - 8 + 17, which simplifies to f(x) = -1 / 3x + 9.