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Question

The function h

 is defined as follows.

h(x)= −x² - 1

If the graph of h is translated vertically upward by 7 units, it becomes the graph of a function f

Find the expression for f(x)

.

Answer 1

"graph of h is translated vertically upward by 7 units, it becomes the graph of a function f" means that the value of f(x) is 7 units more than the value of h(x), for every x [note: h and f are functions).

So,

f(x) = h(x) + 7

f(x) = −x² - 1 + 7

f(x) = −x² + 6

Answer 2

If the graph is translated upward 7 units, the new f(x) would be:

f(x) = -x²-1+7 = -x²+6

f(x) = -x²+6