Question

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x 3)2 4?left 3, up 4right 3, down 4left 3, down 4right 3, up 4

Answer 1

Answer:

Right 3, Down 4

Step-by-step explanation:

Given

$f(x) = x^2$

$g(x) = (x + 3)^2 - 4$

Required

The transformation from f(x) to g(x)

When a function is translated up by h units, the rule is:

$(x,y) \to (x + h,y)$

So, we have:

$f'(x) = (x + h)^2$

By comparison, h = 3. So:

$f'(x) = (x + 3)^2$

When a function is translated down by h units, the rule is:

$(x,y) \to (x,y - h)$

So, we have:

$g(x) = f'(x) -h$

By comparison, h = 4. So:

$g(x) = (x + 3)^2 - 4$

Hence, the transformation is: 3 units right and 4 units down