Questions: Identify the parent function and the transformation shown in the graph. (Select all that apply.) A vertical shift of two units upward. A vertical stretch, two-fold. A horizontal shift of two units to the right. A horizontal shift of two units to the left. A vertical shift of two units downward. Write an equation for the graphed function.

Identify the parent function and the transformation shown in the graph. (Select all that apply.)
A vertical shift of two units upward.
A vertical stretch, two-fold.
A horizontal shift of two units to the right.
A horizontal shift of two units to the left.
A vertical shift of two units downward.

Write an equation for the graphed function.

Transcript text: Identify the parent function and the transformation shown in the graph. (Select all that apply.) A vertical shift of two units upward. A vertical stretch, two-fold. A horizontal shift of two units to the right. A horizontal shift of two units to the left. A vertical shift of two units downward. Write an equation for the graphed function.

Solution

Solution Steps

Step 1: Identify the Parent Function

The given graph resembles the graph of the parent function \( y = \frac{1}{x} \), which is a hyperbola with vertical and horizontal asymptotes at \( x = 0 \) and \( y = 0 \), respectively.

Step 2: Determine the Transformations

The graph shows a vertical shift downward. The vertical asymptote remains at \( x = 0 \), but the horizontal asymptote has shifted from \( y = 0 \) to \( y = -2 \). This indicates a vertical shift of 2 units downward.

Step 3: Write the Equation of the Graphed Function

Given the vertical shift of 2 units downward, the equation of the transformed function is: \[ y = \frac{1}{x} - 2 \]