Question

Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is an equation for g(x)?

Answer 1

`g(x) = 32x - 7`

Explanation:

In `y = afb(x + c) + d`:

•`a` represents the vertical stretch

•`b` represents the horizontal stretch

•`c` represents the horizontal translation

•`d` represents the vertical translation

We are given that `g(x)` has a vertical stretch and a vertical translation (down and up are on the y-axis, hence it's a vertical translation).

Therefore, the equation of `g(x)` is

`g(x) = 4(8x) - 7 =32x - 7`

Practice Exercises

1. Consider the function `f(x) = x^3`. `f(x)` undergoes a vertical transformation of `5` units down and a horizontal translation of `2` units right. It is reflected over the x-axis. What is `f(x)`'s new equation?

2. The point `(6, -4)` lies on the graph of function `g(x)`. What are the coordinates of the point that will lie on `2g(3x - 9) + 1`?

Solutions

1. `f(x) = -(x - 2)^3 + 2`
2. `(5, -7)`

Hopefully this helps!