In Exercises 17-32, use the graph of y = f(x) to graph each funct...

Question

In Exercises 17-32, use the graph of y = f(x) to graph each function g.

Graph of y = f(x) showing a parabola with points at (-4,0), (0,-16), and (4,0).

g(x) = f(x-1)

Accepted Answer

Welcome back. I am so glad you're here. We are given this graph of Y equals f of X. That's this whole graph right here. This lovely looking parabola and we are to use it to graph the function H. Of X. Which is equal to f of parentheses X plus four. So it's very similar. Now let's see how we can get this affects shifted in order to graph an H of X. What's similar? Well from Y equals F of X to R. H. Of X equals f of X plus four. The difference is this plus four happening in here. It's happening directly to our exits inside the function it's in those parentheses. So when the shift is happening directly to our function inside with the X. That indicates a horizontal shift. And specifically because we are adding for it is a horizontal shift to the left or units. So that's what's happening here. If we look at our Y equals F of X. Let's look specifically at where this comes together at the zero negative 16. And that's going to shift to the left. It's going to happen with the other points too. But let's look specifically here so that we have one thing to focus on. So that's going to the left four units. So our X value of zero will be changing to negative four. The Y value negative 16 isn't going to change but we'll look specifically for an H. Of X. That will be a very similar Parabola. It'll be shifted to the left four units. And we can look for that point negative four negative to find the correct answer choice. So let's bring this down answer choice A. That has the 0.4 negative 16 that was shifted to the right instead of to the left. That's not what we're looking for. Sorry. Goodbye answer choice A. We don't want you answer choice B. That did shift to the left. Four units. That has the point negative four negative 16. Great answer choice B. Has potential. Let's rule out C. And D. C. Has four negative 12. That shifted to the right and up. That's not what we're looking for. And answer choice D. Looks like it's shifted to the left and up. It says negative 4 20. That's not even what it looks like. So answer choice D. Just doesn't work on a lot of levels and answer choice B. Does safely work well done. We'll catch you on the next one.

In Exercises 17-32, use the graph of y = f(x) to graph each function g.
g(x) = f(x-1)

Key Concepts

Function Transformation

Graph of a Parabola

Vertex and Intercepts

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