Question

What is the forμla of the function that is shifted left 2 and stretched vertically by a factor of 3 given the following parent function?

(a) ( f(x) = 3(x + 2) )
(b) ( f(x) = 3x - 2 )
(c) ( f(x) = frac13(x + 2) )
(d) ( f(x) = frac13x - 2 )

Answer 1

The formula of the function that is shifted left 2 and stretched vertically by a factor of 3 is f(x) = 3x.

Step-by-step explanation:

The formula of the function that is shifted left 2 and stretched vertically by a factor of 3 can be found by applying the transformations to the parent function.

(a) The parent function is f(x) = 3(x + 2). To shift left 2 units, we need to substitute (x + 2) with (x + 2 - 2) = (x). To stretch vertically by a factor of 3, we need to multiply the function by 3. So, the transformed formula is f(x) = 3x.

Therefore, option (a) (f(x) = 3x) corresponds to the function that is shifted left 2 and stretched vertically by a factor of 3.