Unit 4: Rational & Radical Functions, Booklet 1

2017

pebblebrook high schoolALGBRA 2

4.1 – 4.6

Remember….

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

A dilation is an enlargement or reduction.

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

Transformation Rules

Reference #2: 12 Basic Functions (Parent Graphs)

4.1 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).

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

4.2 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

4.3 Multiplying and Dividing Rational Expressions

How do you simplify 412?

Example #1:

1) Simplify 14 x3 y2

−7 x2 y

2) Simplify 2x−56 x−15

3) Simplify

You Try….

1) Simplify:

2) Simplify:

How do you multiply (23)(614 )?

Steps for Multiplying Rationals

Simplify FIRST (GCF and/or FACTOR) Reduce

Multiply ACROSS Simplify the numerator

Example #2:

1) Multiply

2) Multiply

You Try…..

How do you divide (23) ÷( 614)?

Steps for Divide Rationals

K EEP the 1st fraction. Then simplify C HANGE division to a multiplication. F LIP the 2nd fraction. Then simplify.

Multiply

Example #3:

1) Divide:

2) Divide:

3) Divide:

You Try…..

4.4 Adding & Subtracting Rational ExpressionsHow do you add 57 + 37? How do you add 56 + 37?

Steps for Adding & Subtracting Rational Expressions

FACTOR the denominator Get a common denominator

Add the numerator; keep the denominator the same Simplify

Example #1: Add or Subtract

d. 3x−14 x -

2x−34 x

Example #2: Add or Subtract

a) b)

4.5 Solving Rational Equations

Examples: 1) Solve

2) Solve

3) Solve

You Try…..

4.6 Solving Radical Equations

Steps for solving radicals: ISOLATE the radical Simplify, if necessary. Undo additions/subtractions Undo multiplications/divisions Square/Cube both sides or RECIPROCAL Repeat process, if necessary.

Examples:1) Solve

2) Solve