Question

use a transformation of the graph of \\(y = x^4\\) to graph the function.

\\h(x) = 6(x + 1)^4 + 2\\

choose the correct graph.

Explanation:

Identify the parent function and transformations

$$
LATEXBLOCK0
$$

Determine the specific transformations

$$
LATEXBLOCK1
$$

Locate the transformed vertex/reference point

$$
LATEXBLOCK2
$$

Answer:

To graph the function \(h(x) = 6(x+1)^4 + 2\), apply the following transformations to the parent graph of \(y = x^4\):

1. Shift horizontally left by \(1\) unit.
2. Stretch vertically by a factor of \(6\).
3. Shift vertically up by \(2\) units.

The vertex (or lowest point) of the graph shifts from \((0,0)\) to \((-1, 2)\), and the \(y\)-intercept is at \((0, 8)\).