Question

The graphs below have the same shape. Complete the equation of the bluegraph. Enter exponents using the caret (-); for example, enter x2 as x^2. Donot include "G(x) =" in your answer.GOO = ?FOX0 = x25G(x) =

Answer 1

The question asks us to find the equation of the new graph.

The new graph is the first graph, f(x), only that it was shifted to the left.

In order to shift any graph along the x-axis, you must add or subtract a number from the x-term of the equation.

Shift to right

To shift to the right, we subtract the number of units we want the graph shifted to the right by, from the x-term.

Example; if f(x) = 3x. Then f(x) = 3(x - 5) is a shift to the right by 5 units

Shift to left

To shift to the left, we add the number of units we want the graph shifted to the left by, to the x-term.

Example; if f(x)= 3x. Then, f(x) = 3(x + 5) is a shift to the left by 5 units.

Therefore, we can solve the question asked.

This is done below:

`\begin{gathered} f(x)=x^2 \\ \text{the graph is shifted to the left by 3} \\ \\ \therefore g(x)=(x+3)^2 \end{gathered}`

Therefore, the answer is (x + 3)^2