Question

The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).


G(x)=

Answer 1

Answer:

$g(x)=4x^{2} +10$

Step-by-step explanation:

If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.

Let:

$a>0,\hspace{10}a\in R$

For:

• y = f (x) + a: The graph shifts a units up.
• y = f (x)  - a, The graph shifts a units down.

If:

$f(x)=4x^{2} +6$

and is translated vertically upward by 4 units, this means:

$a=4$

and:

$g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10$

Therefore:

$g(x)=4x^{2} +10$

I attached you the graphs, so you can verify the result easily.