# Section 1.2: Elementary Functions, Graphs and Transformations

## Basic Elementary Functions

 Identity function f(x) = x Square function h(x) = x2 Cube function m(x) = x3 Square root function n(x) = √x Cube root function p(x) = ∛x Absolute value function g(x) = |x|

## Vertical Shifts

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

y = f(x) + k
• Shifts the graph of y = f(x) up k units if k > 0.
• Shifts the graph of y = f(x) down k units if k < 0.

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)
• Shifts the graph of y = f(x) left h units if h > 0.
• Shifts the graph of y = f(x) right |h| units if h < 0.

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

h = 0

## Reflections

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)
• Stretches the graph of y = f(x) vertically by a factor of A if A > 1.
• Shrinks the graph of y = f(x) vertically by a factor of A if 0 < A < 1.

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

A = 1