Question

Which two transformations can be used to obtain the graph of G(x) = -V7+5,from the graph of F(7)= FE?A. A translation to the left five units, followed by a reflection acrossthe x-axis.B. A vertical stretch by a factor of 5, followed by a reflection acrossthe yaxis.C. A translation to the right five units, followed by a reflection acrossthe x-axis.D. A vertical compression by a factor of 5, followed by a reflectionacross the y-axis.

Answer 1

Transformations of a Function

We are given the function:

`G(x)=-\sqrt[]{x+5}`

The parent function of G(x) is:

`F(x)=\sqrt[]{x}`

If we translate F(x) by h units to the right, then if maps to F(x - h).

The radicand of G(x) is x + 5 and it represents a translation of h = -5 units to the right, or equivalently, 5 units to the left.

The minus sign multiplying the square root makes F(x) reflect across the x-axis by inverting its values, thus the two transformations are:

* A translation of 5 units to the left

* A reflection across the x-axis

Choice: A.