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## Graphing a Cube Root Function

**Step 1:** Graph the parent function by creating a table.

**Step 2:** Multiply the y-values by *a*.

**Step 3.** Add/subtract the x-values by *h* and add/subtract the new y-values by *k.*

**Step 4:** Plot the new coordinates and graph the translated/transformed function.

## Graphing a Cube Root Function Vocabulary

**Parent function: ** The simplest function of a family of functions, given in the form {eq}f(x)=\sqrt[3]{x}
{/eq}

The graph and table below represent the parent function.

**The function translation/transformation rules:**

The Translated/Transformed Function is in the form {eq}g(x) =a\sqrt[3]{x-h} +k {/eq}

*a* = Vertical Stretch or Compression.

If a > 1, then it is a Vertical Stretch.

For example, {eq}g(x)=2\sqrt[3]{x} {/eq} is a Vertical Stretch by 2.

If 0 < a < 1, then it is a Vertical Compression.

For example, {eq}g(x)=\frac{1}{2}\sqrt[3]{x} {/eq} is a Vertical Compression by {eq}\frac{1}{2} {/eq}

The following graph compares the Parent Function with a Vertical Stretch by 2 and a Vertical Compression by

{eq}\frac{1}{2} {/eq}

*h* = horizontal translation

If *h* > 0 ,then it is a slide to the right

For example, {eq}g(x)=\sqrt[3]{x-3} {/eq} is a slide to the right by 3 units.

If *h* < 0, then it is a slide to the left.

For example, {eq}g(x)=\sqrt[3]{x+3} {/eq} is a slide to left by 3 units

The following graph compares the Parent Function with a Horizontal Slide to right 3 units and a Horizontal Slide to the left 3 units.

*k* = vertical translation

If *k* > 0, then it is a slide up.

For example, {eq}g(x)=\sqrt[3]{x}+2 {/eq} is a slide up 2 units

If *k* < 0, then it is a slide down.

For example, {eq}g(x)=\sqrt[3]{x}-2 {/eq} is a slide down 2 units

The following graph compares the Parent Function with a Vertical Slide up 2 units and a Vertical Slide down 2 units.

Now let's look at two examples of how to graph a Cube Root Function:

## How to Graph a Cubic Root Function Example 1

Graph {eq}g(x)=3\sqrt[3]{x+4}+2 {/eq}

**Step 1:** Graph the parent function by creating a table.

**Step 2:** Multiply the y-values by the value of *a*, which is 3.

**Step 3:** Subtract the x-values by *h*, which is 4, and add the new y-values by *k*, which is 2.

**Step 4:** Plot the new coordinates and graph the translated/transformed function.

## How to Graph a Cubic Root Function Example 2

Choose the graph of the function{eq}g(x)=4\sqrt[3]{x-3}-2 {/eq}

**Step 1:** Graph the Parent Function by creating a table.

**Step 2:** Multiply the y-values by *a*, which is 4.

**Step 3:** Add the x-values by *h*, which is 3, and subtract the new y-values by *k*, which is 2.

**Step 4:** Plot the new coordinates and graph the translated/transformed function.

The correct answer is Graph 3.