Question

9. The graph of a function p(x) is shown. Draw the graph of -p(x - 1)-3.
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Answer 1

I'll tell you which transformation you have to apply to draw the new graph:

$p(x) \to p(x-1)$

Transformations like $f(x)\to f(x+k)$ translate the function horizontally, k units right if k is negative, k units left if k is positive. In this case, k is negative, so you shift the graph 1 unit to the right.

$p(x-1) \to -p(x-1)$

Transformations like $f(x)\to kf(x)$ stretch the function vertically. If k is negative, they also reflect the graph about the x axis. In this case, k is -1, so you reflect the graph and then stretch with factor 1 (i.e. you don't stretch). So, you reflect the graph about the x axis.

$-p(x-1) \to -p(x-1)-3$

Transformations like $f(x)\to f(x)+k$ translate the function vertically, k units down if k is negative, k units up if k is positive. In this case, k is negative, so you shift the graph 3 unit down.

Follow the bold instruction (in that order!) and you'll have the graph of the new function.