Question

let the graph of g be a vertical stretch by a factor of 6 followed by a translation 2 units left of the graph of f(x)=x²find a rule for g

Answer 1

g(x) = 6 · (x + 2)²

Step-by-step explanation:

If we have a function g(x) = a·f(x), we can say that g(x) is a vertical stretch by a factor of a.

Adittionally, if we have a function g(x) = f(x+c), we can say that g(x) is f(x) translated c units to the left.

Then, if g is a vertical stretch by a factor of 6 followed by a translation of 2 units to the left of f(x), we get that the rule for g(x) is:

g(x) = 6·f(x + 2)

g(x) = 6 · (x + 2)²

Therefore, the answer is:

g(x) = 6 · (x + 2)²