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)= x². Write a rule for g. g(x)= ?

Answer 1

A rule for f(x) after the sequence of transformation is

g(x) = 6(x + 2)²

How to find the rule

To express the rule for the function g(x) obtained by a vertical stretch by a factor of 6 followed by a translation 2 units to the left of the function f(x) = x², you can use the following steps:

Vertical Stretch: Multiply the function by the stretch factor

= 6f(x) = 6x²

Translation 2 units Left

g(x) = 6(x + 2)²