Questions: How can you create a graph that reflects the cubic function across the y-axis? Add -1 to each x-value. Add -1 to each y-value. Multiply each y-value of a function by -1. Multiply each x-value of a function by -1.

How can you create a graph that reflects the cubic function across the y-axis?

Add -1 to each x-value.

Add -1 to each y-value.

Multiply each y-value of a function by -1.

Multiply each x-value of a function by -1.

Transcript text: How can you create a graph that reflects the cubic function across the $y$-axis? Add -1 to each $x$-value. Add -1 to each $y$-value. Multiply each y-value of a function by -1. Multiply each $x$-value of a function by $\mathbf{- 1}$.

Solution

Solution Steps

Step 1: Reflection across the y-axis

To reflect a graph across the y-axis, we need to negate the x-values. This means that for every point (x, y) on the original graph, the reflected point will be (-x, y).

Step 2: Applying the reflection to the function

Let the cubic function be represented as f(x). To reflect the graph across the y-axis, we need to replace x with -x. The reflected function is denoted as f(-x).

Step 3: Choosing the correct option

The question asks how to create a graph that reflects the cubic function across the y-axis. We have determined that this involves replacing x with -x. Therefore, we need to multiply each x-value of the function by -1.