Question

Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value.

Answer 1

Answer:

k=6

Step-by-step explanation:

The parabola that opens up and passes through (-3,-3) will have equation,

$f(x) = {x}^{2} - 12$

The parabola the opens up a d passes through (-3,3) will have equation:

$g(x) = {x}^{2} - 6$

We want to determine the value of k, for which,

$g(x) = f(x) + k$

We rewrite g(x) in terms of f(x) to get:

${x}^{2} - 6 = {x}^{2} - 12 + 6$

$g(x) \to({x}^{2} - 6 )= f(x) \to ({x}^{2} - 12 )+k \to6$

Therefore;

$g(x) = f(x) + 6$

Hence k=6