Questions: Rey graphs the parent function g(x)=x and a transformation of the parent function h(x)=2x^2 on the same coordinate grid. Which statement describes the transformation that occurs between g(x) and h(x)? The graph of h(x) is a vertical translation of the graph of g(x). The graph of h(x) is a horizontal stretch of the graph of g(x). The graph of h(x) is a reflection of the graph of g(x). The graph of h(x) is a vertical stretch of the graph of g(x).

Rey graphs the parent function g(x)=x and a transformation of the parent function h(x)=2x^2 on the same coordinate grid. Which statement describes the transformation that occurs between g(x) and h(x)?

The graph of h(x) is a vertical translation of the graph of g(x).

The graph of h(x) is a horizontal stretch of the graph of g(x).

The graph of h(x) is a reflection of the graph of g(x).

The graph of h(x) is a vertical stretch of the graph of g(x).

Transcript text: Rey graphs the parent function $\mathrm{g}(\mathrm{x})=\mathrm{x}$ and a transformation of the parent function $\mathrm{h}(\mathrm{x})=2 \mathrm{x}^{2}$ on the same coordinate grid. Which statement describes the transformation that occurs between $g(x)$ and $h(x)$ ? The graph of $h(x)$ is a vertical translation of the graph of $g(x)$. The graph of $h(x)$ is a horizontal stretch of the graph of $g(x)$. The graph of $h(x)$ is a reflection of the graph of $g(x)$. The graph of $h(x)$ is a vertical stretch of the graph of $g(x)$.

Solution

Solution Steps

Step 1: Identify the Parent Function and Transformation

The parent function given is $ g(x) = x $, which is a linear function. The transformation function is $ h(x) = 2x^2 $, which is a quadratic function.

Step 2: Analyze the Transformation

To determine the transformation, we need to compare the two functions:

The parent function $ g(x) = x $ is a straight line with a slope of 1.
The function $ h(x) = 2x^2 $ is a parabola that opens upwards with a vertical stretch factor of 2.

Step 3: Determine the Type of Transformation

The transformation from $ g(x) = x $ to $ h(x) = 2x^2 $ involves changing from a linear function to a quadratic function. The quadratic function $ h(x) = 2x^2 $ is a vertical stretch of the basic quadratic function $ x^2 $ by a factor of 2.