7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

1/10

1. Sketch each of the following rational functions, and describe the indicated characteristics. Where possible,graph based on transformations of or . Verify using your graphing calculator.

(a)

(b)

(c)

2. State the equation of any asymptotes for each:(a) (b) (c)

Practice

Vertical Asymptote:

Horizontal Asymptote:

Domain:

Range:

-intercept:

-intercept:

Vertical Asymptote:

Horizontal Asymptote:

Domain:

Range:

-intercept:

-intercept:

Vertical Asymptote:

Horizontal Asymptote:

Domain:

Range:

-intercept:

-intercept:

Topic 4 Rational Functions

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

2/10

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

3/10

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

4/10

Describe the graph of in terms of domain, range, and nature of discontinuities. (Sketch)

Explore 2

Domain: Range:

-intercept: -intercept:

Explore 3

Use your graphing clac. to sketch the function .Set your window to match that provided, obtain points from your calculator and copy the graph here.

On your calculator, use TRACE to determine the value when .Describe the effect on the graph

Factor / simplify the expression. Describe the characteristics of the graph. Make a conjecture of the two types of NPV effects on a rational function graph.

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

5/10

1. For the rational function , sketch and state:(a) Any non-permissible values

(b) Any intercepts

(c) Vertical Asymptote or Point of Discontinuity

(d) Behavior near each NPV

2. For the rational function , sketch and state:(a) Any non-permissible values

(b) Any intercepts

(c) Vertical Asymptote or Point of Discontinuity

(d) Behavior near each NPV

3. State the NPVs and effect on resulting graph (PD or VA) for the following functions:(a) (b)

Practice

(e) Domain and Range

(e) Domain and Range

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

6/10

4. For each of the following functions, factor and simplify to describe the graph characteristics.(a) (b)

5. Write the equation for each rational function:

Domain:Range:

Types of discontinuities (VA or PD):

-intercept: -intercept:

Domain:Range:

Types of discontinuities (VA or PD):

-intercept: -intercept:

(a) (b)

6.

WRONG Equation,

replace the -4 on top

with (x-4)

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

7/10

7.

8.

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

8/10

9.

10.

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

9/10

TOPIC 6 RATIONAL EQUATIONS MATH 30-1 CLASS BOOKLET IV

Like all equations in this course, rational equations can be solved either algebraically, or graphically.

The solutions (or roots) of a radical equation are the same as the -intercpets of the function.

1. Solve each equation algebraically, and verify graphically.(a) (b)

Alberta Ed Learning Outcome: Find the zeros of a rational function graphically and explain their relationship to the -intercepts of the graph and the roots of an equation.

Connect

Consider the equation We can solve this equation:

Algebraically:

Multiply all 3 terms by

the LCD

Graphing:

Option 1

Graph &

Find point(s) ofintersectionCancel / simplify

Solve the resulting quadratic

equation by factoring

Option 2

Graph and find the zeros

The solutions, or roots of a rational equation are

equivalent to the -intercepts of the corresponding

function.

So equations can be solved graphically!

*When solving algebraically watch for extraneous

roots. (We should still verify graphically or by substituting

solutions into the equation)

Practice

7/30/2019 Solutions to RATIONAL FUNCTIONS class handout

10/10

2. Solve each equation graphically, and verify by substituting your solution(s) by substituting into the originalequation.

(a) (b)

3. Solve the following equation graphically, round each solution to the nearest hundredth.