Question

Describe the transformation that takes f(x) = x+1 to g(x) = -x+4.

Answer 1

The sign on the 'x' changes, this implies a reflection.

g(x) = -f(x) = -(x+1) = -x -1

Now apply a vertical translation 'up 5' to f(x)

g(x) = -f(x) + 5 = (-x-1) +5 = -x +4

Hope this helps! <3

Answer 2

Reflecting over the x-axis, vertical movement up 3 units.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

• m - slope

• b - y-intercept

Transformations of graphs

Explanation:

Step 1: Define

f(x) = x + 1

g(x) = -x + 4

Step 2: Define

Multiplying -1 to x flips it over the x-axis, or known as a reflection. There is no vertical shrink/stretch.

To get to 1 to 4, we add 3. That means we will be moving the graph up 3 units.