Question

The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3

Answer 1

The equation of f(x) is

`f(x)=x^2`

The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.

For horizontal translation, we follow the following rule >>>

Let parent function be f(x), then

• f(x+a) is the parent translated "a" units left

,

• f(x-a) is the parent translated "a" units right

Thus, following the rule, we can clearly say that g(x) = f(x+3)

We can write >>