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)"
<h3>
What thing does each transformation?</h3>
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: <em>"function decreases as x increases"</em>
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: <em>"asymptote of y = 2.</em>
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
