Question

Line m is represented by the function f(x) =1 5-2 +3 2NonAfter the transformation, the image, line m', is represented by the1functions g(x) = -f(x+3) +fx Which statements below21describe the transformation from m to m' ? Select all that apply.

Answer 1

Given the function:

`f(x)=(1)/(3)x+(5)/(2)`

After a transformation, we have the function:

`g(x)=(1)/(2)f(x+3)+(1)/(2)`

Let's determine the statement(s) that describe the transformation.

To describe the transformation, apply the transformation rules for function.

Apply the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope and b is the y-intercept

Let's find the y-intercept for f(x).

`\begin{gathered} f(x)=(1)/(3)x+(5)/(2) \\ \\ y-intercept\text{ of f(x) = }(5)/(2) \end{gathered}`

`\begin{gathered} g(x)=(1)/(2)f(x+3)+(1)/(2) \\ \\ y-\text{intercept of g(x) = }(1)/(2) \end{gathered}`

Let's determine the vertical shifts.

The vertical shifts depends on the y-intercepts. Thus, we have:

`\begin{gathered} b=(5)/(2)-(1)/(2) \\ \\ b=(4)/(2) \\ \\ b=2 \end{gathered}`

The difference of the y-intercepts is = 2

Since the difference is greater than 0, the graph is shifted up 2 units

Let's determine the slopes:

`\begin{gathered} \text{slope of f(x) = }(1)/(3) \\ \\ \text{slope of g(x) = }(1)/(2) \end{gathered}`

Let's determine the vertical stretch from the slope.

The vertical stretch depends on the slope.

Since the slope of the transformed function g(x) is gretaer than the slope of f(x), then there is a vertical stretch.

Apply the transformation rule of functions, we have:

f(x + 3) ==> This means a horizontal shift of m 3 units to the left

Therefore, the graph of m is shifted to the left 3 units

Thus, we have the following transformations:

• m is shifted to the left 3 units

,

• m is shifted up 2 units

ANSWER:

• m is shifted to the left 3 units

,

• m is shifted up 2 units