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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Lesson: 3a

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Lesson: 3d

Lesson: 3e

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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+10​​5​​

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)=​−2x​2​​+3x+2​​5x​2​​−13x+6​​

c)

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

2.

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+9​​x−9​​

b)

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

c)

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

d)

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

e)

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

f)

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

g)

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

h)

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

i)

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

j)

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

Graphs of rational functions

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

or

Graphing Rational Functions
Sketch each rational function by determining:

i) vertical asymptote.

ii) horizontal asymptotes

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

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

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

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

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

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

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

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

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

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

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

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

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

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