1. Transformations of graphs
Summary of the four types of transformation

2. Y = f(x) is any function or
equation of a graph.
This example is an cubic
function/equation.
y = f(x)
There are five basic types of transformation of a graph
i.e. five ways we can move the graph or change its shape

3. Point (x, y) becomes point (x, y+a)
y = f(x) + a
y = f(x) +a
Point (x, y) becomes point (x, y+a)
y = f(x) + a
This is a ‘shift’ in the y-direction

4. Point (x, y) becomes point (x-a, y)
y = f(x)
y = f(x+a) -a
Point (x, y) becomes point (x-a, y)
y = f(x+a)
This is a ‘shift’ in the x-direction, opposite to the sign of number a

5. y = f(x)
y = -f(x)
y = -f(x)
This is a ‘reflection’ in the axis, mirror line y = 0
Every y coordinate gets multiplied by -1

6. y = Af(x)
y = f(x)
Notice what happens at the zeros
y = Af(x)
This is a ‘stretch’ in the y-direction, Scale factor A.
Every answer (y-coordinate) gets multiplied by A

7. Notice what happens at the y-intercept
y = f(Ax)
y = f(x)
y = f(Ax)
This is a ‘stretch’ in the x-direction, Scale factor 1/A
Every x coordinate gets multiplied by 1/A, y values stay the same

8. One missing transformation
What about f(-x)
f(x)=x3-3x-1
Reflection across the y axes