Question

MCR3U0 Name: e) Sketch the function 8(x) and state the domain and range of the transformed function g(x). Important: On the same grid, use step-by-step transformations to arrive at the required new function. Use a different colour for each step and include a legend stating the equa tion of each new graph. The transformations should be shown in the following order. 1. Base Graph 2. Vertical reflection/stretch/compression (if any). 3. Horizontal reflection/stretch/compression (if any). st 4 Horizontal and Vertical translations (if any).​

Answer 1

The function 8(x) is a parabola that opens downward and is centered at (0,0). The domain of 8(x) is x∈R and the range of 8(x) is y∈[0,∞).

To arrive at the new function g(x), follow these steps:

Base Graph: The base graph of 8(x) is shown below.

Vertical Reflection: To reflect the parabola about the x-axis, multiply the function by -1. The new function is g(x) = -8(x).

Horizontal Reflection: To reflect the parabola about the y-axis, multiply the function by -1. The new function is now g(x) = 8(-x).

Horizontal and Vertical Translations: To translate the parabola 4 units to the left and 2 units up, add 4 to the x-coordinates and subtract 2 from the y-coordinates. The new function is g(x) = 8(x-4)-2.

The resulting graph is shown below. The domain of g(x) is x∈R and the range of g(x) is y∈[-2,∞).

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