Question

The function g is defined as follows. g(x)=2x^2-5 If the graph of g is translated vertically upward by 3 units, it becomes the graph of a function h. Find the expression for h(x).

Answer 1

Answer: h(x) = 2x^2-2

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Step-by-step explanation:

We shift the graph of g upward by 3 units. This means we add 3 onto g(x) like so

h(x) = g(x)+3

h(x) = (2x^2-5)+3

h(x) = 2x^2-5+3

h(x) = 2x^2-2

All points on g(x) move up by 3 units to get to a point on h(x). For instance, the y intercept (0,-5) on g(x) moves to (0,-2) on h(x).

When we say something like g(x)+3, we effectively mean y+3 to indicate an upward shift of 3 units. Recall that y = g(x) because they are both outputs.