Question

What transformation was not done to the linear parent function, f(x) = x, to get the function g(x) = - 5(x - 3) - 8 ? A. Reflection over the x-axis B. Shift down 8 units C. Horizontal stretch by a factor of 5 D. Shift right 3 units

Answer 1

A. Reflection over the x-axis.

Explanation:

Now, we present how to transform
`f(x) = x` into
`g(x) = -5\cdot (x-3)-8` below:

1)
`f(x) = x` Given.

2)
`f(x-3) = x - 3` Horizontal shift to the right.

3)
`-5\cdot [f(x-3)] = -5\cdot (x-3)` Vertical scale factor.

4)
`-5\cdot f(x-3)-8 = -5\cdot (x-3)-8` Vertical shift downwards.

5)
`g(x) = -5\cdot (x-3)-8` Definition/Result

In consequence, the only transformation which was not done to the linear parent function was a reflection over the x-axis. The correct answer is A.