Question

Given the function f(x) = 2x^5 - x^3 + x^2 + 4, reflect it in the y-axis and apply a vertical stretch by a factor of 3. What is the new function?

Answer 1

To reflect the function in the y-axis, replace x with -x in the original function. Then, multiply the entire function by 3 to apply a vertical stretch.

Step-by-step explanation:

To reflect the function in the y-axis, we replace x with -x in the original function. So, the reflected function is f(-x) = 2(-x)^5 - (-x)^3 + (-x)^2 + 4. Simplifying this expression gives us f(-x) = -2x^5 + x^3 + x^2 + 4.

To apply a vertical stretch by a factor of 3, we multiply the entire function by 3. So, the new function is g(x) = 3(-2x^5 + x^3 + x^2 + 4). Simplifying this expression gives us g(x) = -6x^5 + 3x^3 + 3x^2 + 12.