Question

Using complete sentences, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is;
y=a^(3)/sqrt(x-h+k)

Answer 1

Three possibilities

For red line

If h is negative then and k is positive then

then they will have two vertical asymptotes one on positive x and other on negative x

If h is negative and k is negative then the side part underroot with x turns negative I e x-(something) then they will form parabolas

You may look purple one

For all values of negative sum of h and k

example √x-k

The graph is parabola (Green one)

For h and k are equal the denominator yields √x and it stops at origin on downwards .(Blue one)

For all values of positive sum of h and k eg denominator as √x+k the graph will be like red one

Answer 2

Answer:

Standard Form of a Cube Root Function

$y=a \sqrt[3]{x-h}+k$

The parent function is $y=\sqrt[3]{x}$

$h$ indicates the horizontal shift from the parent function.
If $h > 0$ the shift is to the right, and if $h < 0$ the shift is to the left.

$k$ indicates the vertical shift from the parent function.
If $k > 0$ the shift is up, and if $k < 0$ the shift is down.

$a$ indicates a vertical stretch by scale factor $a$.  
If $a < 0$ the function is reflected in the x-axis.