In Exercises 55–59, use the graph of to graph each function g.

Question

Graph showing the transformation of g(x) = -f(2x) with x and y axes labeled.

g(x) = -f(2x)

Accepted Answer

Welcome back. I am so glad you're here. We are given this function. Why equals F. Of X. And it's drawn here. And we need to with use that to graph the function G. Of X equals F of X divided by two plus one. So what's the difference between our F. Of X and our G. Of X? While there are a couple of things happening here, this X inside is being divided by two. And here we have a plus one happening. So what do each of those mean starting closest to the X. What's happening here directly to the X? Is that it's being divided by two? Or being multiplied by one half? Because it's being multiplied directly by a number that is between zero and one. This indicates that when it's happening directly to the X. It's horizontal shift. And because it's being multiplied by a number between zero and 1, it indicates stretching. So we have horizontal stretching taking place. What about this? Plus one happening off to the end of our equation. Well that's not happening directly to the exits, not inside the parentheses. So that indicates a vertical shift. And because one is being added, that indicates it's going to go up one unit from where it encounters the origin. So we see that this F. Of X is at the origin here at 00. And because our G of X is going up one, then it's going to start the function at 01. It'll be a chain for the Y axis. So let's look at our answer choices and see if any of them have that shift. They start at 01 and have some vertical or excuse me, horizontal stretching. So looking at our answer choices anything starting at 01. Well, answer choice A. Does begin at 01. Answer choice B. Does not. That begins at negative 20 answer choice C. Begins at negative 10, and answer choice D. Begins at 0.5. So our correct answer choice here is answer choice A. Well done. We'll catch you on the next one.

In Exercises 55–59, use the graph of to graph each function g.
g(x) = -f(2x)

Key Concepts

Function Transformation

Reflection Across the X-Axis

Horizontal Compression

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