Unit 4: Rational & Radical Functions, Booklet 1

2017

pebblebrook high schoolALGBRA 2

4.1 – 4.3

4.1 Graphing “Fred” Functions

Functions can be represented in 3 ways: a table of points, graph, or an equation.

There are 12 basic functions that are studied between Algebra 2 & Precalculas (p. )

For each function, you should be able to identify the key characteristics from the graph AND algebraically.

Additionally, you should be able to graph these functions as well.

Definition of a “Fred” Function – the name given to a function if it is NOT one of the basic 12 functions.

Objective: Graph “Fred” functions using transformations rules.

Translation: - a slide up, down, left, right, or combination.

Example #1: Complete the table and plot the new coordinates.

x f(x) f(x) + 4

State the domain: __________ State the range: _________

Think, Pair, Discuss…

Functions can be represented in 3 ways: a table of points, graph, or an equation.

There are 12 basic functions that are studied between Algebra 2 & Precalculas (p. )

For each function, you should be able to identify the key characteristics from the graph AND algebraically.

Additionally, you should be able to graph these functions as well.

Example #3: Complete the table and plot the new coordinates.

Think, Pair, Discuss…

Example #4: Complete the table below.

x f(x) f(x + 4)

Remember….

A reflection is a flip over the y-axis, x-axis or a combination.

A dilation is an enlargement or reduction.

Example #5: Complete the table below

Reflections & Dilations

Example #1: Complete the table and plot the new coordinates.

x f(x) -f(x)

Example #2: Complete the table and plot the new coordinates.x f(x) f(-x)

Example #3: Complete the table and plot the new coordinates.x f(x) 3f(x)

Reference #2: 12 Basic Functions

Section 4.1 Homework

4.2 Graphing Rational Functions

Parent function f(x) = 1xF(x) = a

x−c + h

Sometimes called the inverse function.Important parts:

Vertical asymptote – the vertical “line” of discontinuity; algebraically, x = c.

Horizontal asymptote – the horizontal “line” of discontinuity; algebraically, y = h.

Domain = (-∞, c) ∪ (c, ∞) Range = (-∞, h) ∪ (h, ∞) Vertical stretch if a ¿1 Vertical shrink if o<a<1 Reflection: y-axis or x-axis

Example #1: Describe the rational functions.

You Try…..

Example #2: Sketch the graph of the rational function.

You Try….

When f(x) = P(x )Q(x) = a x

n+…..bxm+… , then

a) Vertical asymptote are the zeros of the DENOMINATOR.

b) Horizontal asymptotes follow the these rules:

If n = m, Y = abIf n ¿ m, Y = 0If n ¿ m, NO Horizontal

asymptote

Example #3: Find the vertical & horizontal asymptote(s).

Section 4.2 Homework

4) Sketch the graph and describe the function.

5) Sketch the graph and describe the function.

6) Find the vertical and horizontal asymptotes.

7) Find the vertical and horizontal asymptotes.

8) Find the vertical and horizontal asymptotes.

Vertical Asymptote(s) Horizontal Asymptote

Vertical Asymptote(s) Horizontal Asymptote

Vertical Asymptote(s) Horizontal Asymptote

Important Parts:

Start Coordinate (c, h)

x-intercpets

y-intercepts

Domain: [c, ∞) or (−∞ , c]

Range: [h, ∞) or (-∞, h]

Vertical stretch if a ¿1

Vertical shrink if o<a<1

Reflection: y-axis or x-axis

Important Parts:

Start Coordinate (c, h)

Domain: (-∞, ∞ ¿

Range: (-∞ ,∞)

Vertical stretch if a ¿1

Vertical shrink if o<a<1

Reflection: y-axis or x-axis

4.3 Graphing Radical FunctionsSquare root functions: f(x) = a√ x−c - h

Cube root functions: f(x) = 3√ x−c – h

Examples: Describe the function. Then graph.1. f ( x )=2√ x−3+2 2. f ( x )=−√x+2−2Description: _____________ Description: __________________

_________________________ _____________________________

Start Point: _____________ Start Point: _____________

Domain: ______________ Domain: __________________

Range: _______________ Range: ____________

Vertical Stretch: __________ Vertical Stretch: ___________

Vertical Shrink: ___________ Vertical Shrink: ____________

Reflection: _____________ Reflection: ______________

3. f ( x )=−1

3 √x−4

Section 4.3 Homework Describe the function. Then graph.