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The graph of $ f $ is given. Draw the graphs of the following functions.

(a) $ y = f(x) - 3 $

(b) $ y = f (x + 1) $

(c) $ y = \frac{1}{2} f(x) $

(d) $ y = -f(x) $

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Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Okay, so here we have a sketch of our graph and we want to graph y equals F of X minus three. So we're going to take the original graph and shifted down three units, and I like to do that by taking the key points, the end points of the segments and shifting them down first. So the endpoints go down three and then we can connect them. And that's our graph for part A. For part B, this transformation is going to be a shift left one. So I'm going to do the same kind of thing where I'm going to take the key points, the end points of the segments, and shift them, left one, and then connect them, and that will shift the entire graph left one. So that's our graph for part B. And the transformation taking part in part C is a vertical shrink by a factor of two, so the graph will be half as tall. So what we're going to do is take those key points and cut their Y coordinates in half. So if we have a point with a white coordinated to its now, gonna be one a point with a white coordinative zero. Still zero a point with a Y coordinate of three. Now that's 1.5 and a point with a Y coordinate of two. Now that's one. And then we connect those and we get a graph that's half is tall. Same width noticed. No change to the width on lee. A change to the height Never part D. What we have here is a reflection about the Y axis. Excuse me about the X axis. Okay, so we're going to take each of the key points and reflected across the X axis. So point at a height of two is now going to be a height of negative, too. A point at a height of zero is still zero a point at a height of three is now at negative three and a point at height of two is now negative too. And then we connect those points and we have our reflected graph