Question

the function g is defined as follows.
\\( g(x) = 2x^2 - 8 \\)
if the graph of g is translated vertically upward by 5 units, it becomes the graph of a function h.
find the expression for \\( h(x) \\).
note that the aleks graphing calculator may be helpful in checking your answer.
\\( h(x) = \square \\)

Explanation:

Step1: Recall vertical translation rule

For a function \( y = f(x) \), a vertical upward translation by \( k \) units gives \( y = f(x)+k \). Here, \( g(x)=2x^{2}-8 \) and \( k = 5 \).

Step2: Apply the translation to \( g(x) \)

To find \( h(x) \), we add 5 to \( g(x) \). So \( h(x)=g(x)+5=(2x^{2}-8)+5 \).

Step3: Simplify the expression

Simplify \( (2x^{2}-8)+5 \) to get \( 2x^{2}-3 \).

Answer:

\( h(x)=2x^{2}-3 \)