Graphs of rational functions - Rational Functions

Graphs of rational functions

Lessons

1.
Graphing Rational Functions
Sketch each rational function by determining:

i) vertical asymptote.

ii) horizontal asymptotes
3.
Identifying Characteristics of Rational Functions
Without sketching the graph, determine the following features for each rational function:

i) point of discontinuity

ii) vertical asymptote

iii) horizontal asymptote

iv) slant asymptote

Graphs of rational functions

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Don't just watch, practice makes perfect

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Lessons

1.

Graphing Rational Functions Sketch each rational function by determining: i) vertical asymptote. ii) horizontal asymptotes

a)

f(x)=52x+10f\left( x \right) = \frac{5}{{2x + 10}}f(x)=2x+105​

b)

g(x)=5x2−13x+6−2x2+3x+2g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}g(x)=−2x2+3x+25x2−13x+6​

c)

h(x)=x320x−100h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}h(x)=20x−100x3​

2.

Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes Sketch the rational function f(x)=2x2−x−6x+2f(x) = \frac{2x^{2}-x-6}{x+2}f(x)=x+22x2−x−6​ by determining: i) points of discontinuity ii) vertical asymptotes iii) horizontal asymptotes iv) slant asymptote

3.

Identifying Characteristics of Rational Functions Without sketching the graph, determine the following features for each rational function: i) point of discontinuity ii) vertical asymptote iii) horizontal asymptote iv) slant asymptote

a)

a(x)=x−9x+9a(x) = \frac{x - 9}{x + 9}a(x)=x+9x−9​

b)

b(x)=x2−9x2+9b(x) = \frac{x^{2}-9}{x^{2}+9}b(x)=x2+9x2−9​

c)

c(x)=x2+9x2−9c(x) = \frac{x^{2}+9}{x^{2}-9}c(x)=x2−9x2+9​

d)

d(x)=x+9x2−9d(x) = \frac{x+9}{x^{2}-9}d(x)=x2−9x+9​

e)

e(x)=x+3x2−9e(x) = \frac{x+3}{x^{2}-9}e(x)=x2−9x+3​

f)

f(x)=x2+9x+9f(x) = \frac{x^{2}+9}{x+9}f(x)=x+9x2+9​

g)

g(x)=−x−9−x2−9g(x) = \frac{-x-9}{-x^{2}-9}g(x)=−x2−9−x−9​

h)

h(x)=−x2−9−x2+9h(x) = \frac{-x^{2}-9}{-x^{2}+9}h(x)=−x2+9−x2−9​

i)

i(x)=x2−9x+3i(x) = \frac{x^{2}-9}{x+3}i(x)=x+3x2−9​

j)

j(x)=x3−9x2x2−3xj(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}j(x)=x2−3xx3−9x2​

Graphs of rational functions

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or

Graphing Rational Functions
Sketch each rational function by determining:

i) vertical asymptote.

ii) horizontal asymptotes

$f\left( x \right) = \frac{5}{{2x + 10}}$

$g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}$

$h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}$

Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes
Sketch the rational function

$f(x) = \frac{2x^{2}-x-6}{x+2}$

by determining:
i) points of discontinuity
ii) vertical asymptotes
iii) horizontal asymptotes
iv) slant asymptote

Identifying Characteristics of Rational Functions
Without sketching the graph, determine the following features for each rational function:

i) point of discontinuity

ii) vertical asymptote

iii) horizontal asymptote

iv) slant asymptote

$a(x) = \frac{x - 9}{x + 9}$

$b(x) = \frac{x^{2}-9}{x^{2}+9}$

$c(x) = \frac{x^{2}+9}{x^{2}-9}$

$d(x) = \frac{x+9}{x^{2}-9}$

$e(x) = \frac{x+3}{x^{2}-9}$

$f(x) = \frac{x^{2}+9}{x+9}$

$g(x) = \frac{-x-9}{-x^{2}-9}$

$h(x) = \frac{-x^{2}-9}{-x^{2}+9}$

$i(x) = \frac{x^{2}-9}{x+3}$

$j(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}$