Question

3. The function f(x) = x^3 undergoes the following transformations: horizontal reflection

vertical expansion by a factor of 4 and then translated 2 unit up and 10 to the
right. Write the equation of the image function (this is the final function).

Answer 1

f(x) = -4(x - 10)^3 + 2.

Explanation:

Parent function f(x) = x^3.

The horizontal reflection gives the function -x^3.

The vertical expansion factor 4 gives the function -4(x)^3.

Translation of 2 up gives -4(x)^3 + 2.

Translation of 10 to the right gives f(x) = -4(x - 10)^3 + 2.