Question

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Given the function f(x) = x2 and k = –3, which of the following represents a vertical shift...

f(x) + k
kf(x)
f(x+k)
f(kx)

Answer 1

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Answer 2

Think about how the graph of y=x looks like compared to y=x+3.
How about y=x^2 compared to y=x^2-7

In general, adding a constant to a function shifts it vertically.

Choice b dilates the graph depending on the value of k.
If k is a positive real number > 1 the graph will be stretched vertically (and thus compressed horizontally), for example.
If k is a number < 1 but > 0, then the graph is compressed vertically and stretched horizontally (it becomes wider)

Choice c moves the graph horizontally. Usually it is written as f(x-k), where the graph is moved k units. If k is positive, it's to the right, if it's negative (which will cause it to be f(x-(-k)) = f(x+k)) then it's to the left.

Choice d dilates the graph too, but in the opposite way that b does. So if k is a positive real number > 1, then the graph will be dilated **horizontally** by k, but **vertically** by 1/k. In other words, it will be compressed/become wider like in choice b.
If k is a number <1 but >0, then the graph is stretched vertically.