Question

The function his defined as follows.h(x) = 2x ^ 2 + 5If the graph of his translated vertically upward by 4 units, it becomes the graph of a function f.Find the expression for f(x)

Answer 1

Solution

Given that the function below

$h(x)=2x^2+5$

The graph of h(x) is shown below

If the graph of h(x) is translated vertically upwards by 4 units to give the function f(x), the function f(x) will be

$\begin{gathered} f(x)=2x^2+5+4=2x^2+9 \\ f(x)=2x^2+9 \end{gathered}$

Hence, the graph of f is

Hence, the expression for f(x) is

$f(x)=2x^2+9$