Common Rational Functions Absolute Value Function Reciprocal Function

Common Rational Functions Absolute Value Function Reciprocal Function Square Root Function Cusp

• The vertex is at ( h, k) • The axis of symmetry is x=h • The graph has a vertical shift of k

Transformation of Absolute Value Function Right 2 units Refence Point Transformation Down 3 units New Point

Refence Point Transformation New Point

Your Turn Refence Point Transformation New Point

Your Turn Refence Point Transformation New Point

Refence Point Transformation New Point

• the y-axis is a vertical asymptote • the x-axis is a horizontal asymptote. Notice that for this function • A small positive input value yields a large positive output value. • A large positive input value yields a small positive output value. § A small negative input will output a large negative value § A large negative input will output a small negative value.

Domain Range Form for Transformations REFERENCE POINTS

YOUR TURN EXAMPLE 1 Refence Point Transformation New Point

YOUR TURN List the transformation on the parent function & state the domain & range and then graph. Vertical reflection over the x-axis 2 units horizontally left 5 units vertically down

Refence Point Transformation New Point

YOUR TURN List the transformation on the parent function & state the domain & range and then graph

Refence Point Transformation New Point

Reference Transformation Point (x +1, 2 y +3) New Point

Using the graph shown, write the equation and describe the transformation g is f reflected across the yaxis and translated 3 units up.

Inverse Squared

Reference Transformation Point (x +3, y) New Point

Reference Transformation Point (x -5, 2 y-5) New Point

Graph What is the amplitude of the function? Are there any asymptotes?

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve , which has a cusp at the origin.