Section 1.2: Elementary Functions, Graphs and Transformations

Basic Elementary Functions

Identity functionf(x) = x
Square functionh(x) = x2
Cube functionm(x) = x3
Square root functionn(x) = √x
Cube root functionp(x) = ∛x
Absolute value functiong(x) = |x|

Vertical Shifts

Adding a constant k to the function f(x):

y = f(x) + k

Drag the slider to add or subtract a constant k to the function.

k = 0

Horizontal Shifts

Adding a constant h to the value of x in the function f(x):

y = f(x + h)

Drag the slider to shift the function a constant h left or right.

h = 0


Multiplying the function f(x) by -1:

y = -f(x)

This reflects the graph of y = f(x) in the x axis.

Stretches and Shrinks

Multiplying the function f(x) by a constant A:

y = Af(x)

Drag the slider to multiply the function by a constant A.

A = 1