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

Answer:

A. Reflection over the x-axis.

Step-by-step 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.