Question

The graphs below have the same shape. What is the equation of the graph of g(x)?

Answer 1

Answer:

A

Step-by-step explanation:

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

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Here g(x) is the graph of f(x) = x²  shifted 4 units to the left, hence

g(x) = (x + 4)² → A

Answer 2

The equation of the function g(x) based on the translation of f(x) is g(x) = (x + 4)²

How to determine the translation?

The function f(x) is given as:

f(x) = x²

The function f(x) is translated 4 units left to get function g(x)

This means that:

g(x) = f(x + 4)

So, we have:

f(x + 4) = (x + 4)²

This gives

g(x) = (x + 4)²

Hence, the equation of the function g(x) based on the translation of f(x) is g(x) = (x + 4)²

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