Question

To graph the function g(x)=^3sqrt(-x-11) start with the graph f(x)=^2sqrtx then make which of the following changes?


A. Shift the graph of left by 11 units.
B. Shift the graph of right by 11 units.
C. Shift the graph of up by 11 units.
D. Shift the graph of down by 11 units.
E. Reflect the graph of over the -axis.
F. Reflect the graph of over the -axis.
G. Stretch the graph of horizontally.
H. Stretch the graph of vertically.

Answer 1

@aaronq you there?

Answer 2

now, \(f(x)=^{2}\sqrt{x}=(x)^{\frac{1}{2}}\) and \(p(x)=^{3}\sqrt{x}=(x)^{\frac{1}{3}}\)

If we take a point, x=9,

\(f(x)=(9)^{\frac{1}{2}} = 3\)

\(p(x)=(9)^{\frac{1}{3}}\approx 2.1 \)

So we see that f(x) is travelling faster in the y direction, this is a vertical stretch.

now \(g(x)=\sqrt{(-x-11)}\), if we let x=0, we get \(\sqrt{-11}\), which doesnt exist in real numbers. So "-x-11=0" must be met. \(x\leq -11\)

SO the vertex is at, x=-11, and the graph is reflected on the y-axis, (because values of x can only be less than -11 and the y-values stay positive).