<p>P790, problem 20. what is the best way to do it? Please help me!</p>
<p>A quick review of shifts:</p>
<p>Verical shift up: f(x) + k
Vertical shift down: f(x) - k
Horizontal shift left: f(x + k)
Horizontal shift right: f(x - k)</p>
<p>Note: k is a positive constant</p>
<p>Can you get the answer now?</p>
<p>Nice explanation DrSteve, could you give an explanation for what to do when they make the functions like 2f(x) = y? I’d greatly appreciate it.</p>
<p>@piratebay, 2f(x) = y, e.g. if f(x) = 5x + 1 then 2(5x+1) = y.</p>
<p>(I don’t have the blue book)</p>
<p>The graph of 2f(x) is an “expansion” of the graph of f(x). All the y coordinates are doubled. If you graph f(x) and 2f(x) separately they pretty much look identical. But if you graph them on the same set of axes, then 2f(x) rises twice as fast as f(x) (or falls twice as fast if the points are below the x-axis)</p>
<p>More generally we have the following:</p>
<p>kf(x) is a vertical expansion if k > 1 and a vertical contraction if 0 < k < 1
f(kx) is a horizontal contraction if k > 1 and a horizontal expansion if 0 < k < 1</p>
<p>We handle minus signs separately:</p>
<p>-f(x) is a reflection in the x-axis
f(-x) is a reflection in the y-axis</p>
<p>More complex examples:</p>
<p>-3f(x) is an expansion by 3, followed by a relection in the x-axis (or you can do it in the other order)</p>
<p>f(2 - x) + 3</p>
<p>do this in the following order:
f(x)
f(x - 2)
f(-(x - 2)) = f(2 - x)
f (2 - x) + 3</p>
<p>So we see that this is a shift right 2, followed by a reflection in the y-axis, followed by a shift up 3.</p>
<p>Thank you !</p>
<p>So I got h = - 3, since g shifted 3 units right from f, and k = -2, since g shifted 2 unit down from f. Therefore hk = +6. makes perfect sense. Thanks! :)</p>
<p>That’s exactly right. Knowing these basic shifts will make some of those last difficult function questions quite easy.</p>