Question

use a transformation of the graph of \\(y = x^5\\) to graph the function.

\\h(x) = -x^5\\

choose the correct graph.

Explanation:

Identify the base function

The given base function is:

$$y = f(x) = x^5$$

Analyze the transformation

Using the Function Transformations knowledge point, we analyze the target function:

$$h(x) = -x^5 = -f(x)$$

Multiplying the output of a function by \(-1\) reflects its graph vertically across the x-axis.

Determine key coordinate points

We calculate key points for both the base function and the transformed function:

• For \(y = x^5\):
• \((-1, -1)\)
• \((0, 0)\)
• \((1, 1)\)
• For \(h(x) = -x^5\):
• \((-1, 1)\)
• \((0, 0)\)
• \((1, -1)\)

Describe the final graph

The graph of \(h(x) = -x^5\) starts in the second quadrant, passes through the origin \((0,0)\), and goes down into the fourth quadrant.

Answer:

The graph of \(h(x) = -x^5\) is obtained by reflecting the graph of \(y = x^5\) vertically across the x-axis.

Key points on the graph of \(h(x)\) include:

• \((-1, 1)\)
• \((0, 0)\)
• \((1, -1)\)