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

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.