If the graph of the function g defined by g(x)= -x^2-7 is translated vertically upward by 8 units, it becomes the graph of a function h. Find the expression for h(x).

Answer 1

Hello Alyssa,

Let g(x) be a function, and k any real number. Then the graph of the function h(x) = g(x) + k is obtained by translating the graph of g(x) by k units in the vertical direction. So to obtain the expression for the desired function h(x) in your problem, you will simply add 8 to the expression for g(x). That is,

h(x) = g(x) + k

h(x) = g(x) + 8

h(x) = (-x² - 7) + 8

h(x) = -x² + 1.

Hope that helps!

William

Answer 2

In order to shift a graph vertically, you add a number to the expression for x.

For example, y=mx+b is shifted up by b.

y=x^2+k is moved up by k

y=x^2-k is moved down by k

y=-x^2-7 is shifted down by seven. To shift,or translate, y=-x^2-7 up by 8, you can add 8 to the equation.

You get h=-x^2-7+8 or h=-x^2+1. So h(x)=-x^2+1