There are **six **transformations that you can perform on the graph of a function.

Let’s look at what happens when we apply these to the function** y = sin (x) 0 ≤ x ≤ 360**

The results will be the same for the functions y = cos (x) and y = tan (x).

**f(x) → f(x) + a {Translation with a vector of **

**}**

Sin (x) → sin (x) + 1 has the effect of moving the graph upwards by 1.

**f(x) → f(x + a) { Translation with a vector of **

**}**

Sin (x) → sin (x + 90) has the effect of moving the graph left by 90°.

This transforms y = sin(x) into y = cos(x).

**f(x) → af(x) **{**Stretch****in the y-axis, scale factor a****}**

Sin (x) → 2sin (x) has the effect of increasing every value of y by 2. It stretches the graph vertically.

**f(x) → f(ax) { Stretch in the x-axis, scale factor 1/a**

**}**

Sin (x) →** **sin (2x) has the effect of multiplying every value of x by 1/2. It compresses the graph horizontally.

**f(x) → -f(x) { Reflection in the x-axis**

**}**

Sin (x) → -sin (x) has the effect of reflecting the entire graph in the x-axis.

**f(x) → f(-x) {Reflection in the y-axis**

**}**

Sin (x) → sin (-x) has the effect of reflecting the entire graph in the y-axis.

In the case of transforming sin (x), you have probably noticed that **sin (-x) = - sin(x). **

Now it's time for some questions!