Question

20 POINTS Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g. Select ALL of the correct answers.

reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit

shift right 1 unit, reflect over the x-axis, and then vertically stretch by a factor of 3

shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3

shift down 1 unit, reflect over the x-axis, and then vertically stretch by a factor of 3

shift left 2 units, reflect over the x-axis, and then vertically stretch by a factor of 3

reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Answer 1

The correct sequences of transformations to obtain the graph of \( g \) from the parent function \( f(x) = x \) are:

1. **Reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit**
2. **Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit**

Answer 2

- reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit

- shift down 1 unit, reflect over the x-axis, and then vertically stretch by a factor of 3

Explanation:

-This sequence of transformations would reflect the graph of f(x) = x over the x-axis, vertically stretch it by a factor of 3, and then shift it down 1 unit. This transformation sequence would truly produce the graph of g.

-This sequence of transformations would shift the graph of f(x) = x down 1 unit, reflect it over the x-axis, and then vertically stretch it by a factor of 3. This transformation sequence would truly produce the graph of g.

glad to help.