function behavior

f(x+c)

horizontal shift to the left c units

f(x-c)

horizontal shift to the right c units

f(x)+c

vertical shift upwards “c” units.

f(x)-c

vertical shift downwards “c” units.

-f(x)

the negative is outside

function flips vertically over the x axis.

f(-x)

the negative is inside, therefore the function flips horizontally over the y-axis.

C*f(x) where C>1. C is greater than 1

vertically stretches the function by a factor of C.

Cf(x) where c<1

compresses the function

Is Cos(x) even or odd?

Cos(x) is even as Cos(-x) = Cos(x)

Is Sin(x) even or odd?

Sin(x) is odd as Sin(-x) = -Sin(x)

Is Tan(x) even or odd?

Tan(x) is odd as Tan(-x) = -Tan(x)

f(cx) where c>1 (c is greater than 1)

squishes the function horizontally

f(cx) where 0<C<1. C is between 0 and 1

the function widens.