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</a></p>
<p>How should I solve this?</p>
<p>Thanks</p>
<p>Review the part in your book on function transformations. Shifting the function down would be subtracting (to give you a hint).</p>
<p>You're shifting a function. By examining that graph, you can see that g(x) seems to be the exact same as f(x), except that g(x) is pushed upward by one unit.</p>
<p>In general, you can shift any function up, down, left, or right quite easily. Say you have some function a(x).
a(x) + 1 is the same as a(x), but shifted up by one unit.
a(x) - 1 is the same as a(x), but shifted down by one unit.
a(x - 1) is the same as a(x), but shifted right by one unit.
a(x + 1) is the same as a(x), but shifted left by one unit.</p>
<p>So, an addition outside the function is shifting vertically (positive is up, negative is down), and an addition within the function is shifting horizontally (positive is left, negative is right--remember this, as it is counterintuitive to many people!).</p>
<p>In your graph, g(x) is the same as f(x) shifted upward by one unit.</p>
<p>Yes, I recognise that g(x) is only another f(x) moving up, yet I usually get confused with which element could shift it up and which could shift it down, left or right. Perhaps learning by heart is the most terrible thing in Math (as well as in other subjects :) )</p>
<p>Something that usually helps me remember shifts like this is trying to graph a relatively simple equation, and then applying the shift and plugging in values to see what happens. I usually use a(x) = x^2, because it is distinctive enough in shape, but still fairly simple.</p>
<p>Without shifts: a(-2) = 4, a(-1) = 1, a(0) = 0, a(1) = 1, a(2) = 4.</p>
<p>With a(x) + 1: a(-2) + 1 = 5, a(-1) = 2, a(0) = 1, a(1) = 2, a(2) = 5.</p>
<p>With a(x-1): a(-2-1) = a(-3) = 9, a(-1-1) = a(-2) = 4, a(0-1) = a(-1) = 1, a(1-1) = a(0) = 0, a(2-1) = a(1) = 1.</p>
<p>Looking at these values, it's a bit easier (at least for me, usually) to see what's really going on with the graph when applying shifts. But maybe that's just something weird that I do...I don't know if it would help anybody else.</p>
<p>Oh no, you are not weird believe me. I have a friend who relax during break time by multiplying randomly 2 billion numbers in a blank paper. He does this nearly all his life so he is as quick as a calculator, ha, ha. We are all weird, aren't we, since this makes us who we are.</p>
<p>inside the parentheses is right (-) or left (+)</p>
<p>outside the parentheses is up (+) or down (-) </p>
<p>It's pretty intuitive after some practice.</p>