Question

Match each transformation of function f to a feature of the transformed function.

Answer 1

By analyzing the parent function graph, we will see that:

• 1) m(x) = -f(x) ⇒  "function decreases as x increases"
• 2)  h(x) = f(x) + 2 ⇒ "asymptote of y = 2"
• 3) j(x) = f(x + 2) ⇒ "y-intercept at (0, 4)"
• 4)  g(x) = 2*f(x)  ⇒ "y-intercept at (0, 2)"

What thing does each transformation?

Let's list each transformation and let's see which is the correct option for each one.

1) m(x) = -f(x).

This is a reflection over the x-axis, so, now the curve will open downwards. This means that now we have a decreasing function, so the correct option here is: "function decreases as x increases"

2) h(x) = f(x) + 2

This is a vertical translation of 2 units upwards. So it moves the whole graph 2 units upwards. Originally, you can see that in the left side we have an asymptote at y = 0, now that asymptote will be at y = 2.

So the correct option is: "asymptote of y = 2.

3) j(x) = f(x + 2)

This is a shift of 2 units to the left, notice that when we evaluate this in x =  0 we et:

j(0) = f(2) = 2^2 = 4

So the y-intercept os (0, 4).

4) g(x) = 2*f(x)

This is a vertical stretch of scale factor 2.

When we evaluate this in x = 0, we get:

g(0) = 2*f(1) = 2

So the y-intercept is at (0, 2).

If you want to learn more about transformations, you can read:

brainly.com/question/4289712