Question

Let f(x) = x^2 +3.

Answer 1

Answer:

It is translated left 6 units

Step-by-step explanation:

I will help you understand graphing a function.

1. Each part in the equation represents how the graph will look.

In the first equation you have an $x^{2}$ and the number 3.

In the second equation you have an $(x + 6)^{2}$and that same number 3.

2. First look at the variable: the $x^{2}$ tells us that both of these functions are positive quadratics opening up

3. The number on the outside tells you where the function is located on the y-axis (vertical movement)

Both equations have the number 3 so the graph will be 3 units high

4. The number on the inside with the variable determines the horizontal movement of the graph

The second equation has a (x + 6)

It might be confusing to think that since its addition the graph should go to the right but it actually goes to the left.

A good saying, I keep in my head is that parenthesis lie (x + 6) really mean 6 units to the

I will also add an image of the graph of the function below.

Answer 2

Answer:

translated left by 6 units

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then shift left of a units

• If a < 0 then shift right by a units

g(x) = (x + 6)² + 3

Indicating a shift of f(x) to the left by 6 units