Topics
4. Rational Functions and Equations
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United States of America
Grades 9-12

4.01 Rational functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the function $y=\frac{1}{x}$y=1x​ which is defined for all real values of $x$x except $0$0.

a

Complete the following table of values.

$x$x $-2$−2 $-1$−1 $-\frac{1}{2}$−12​ $-\frac{1}{4}$−14​ $\frac{1}{4}$14​ $\frac{1}{2}$12​ $1$1 $2$2
$y$y $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Plot the points from the table of values.

Loading Graph...
c

Now draw a graph of the rational function.

Loading Graph...
d

In which quadrants does the graph lie?

$1$1

A

$2$2

B

$3$3

C

$4$4

D
Medium
2min

Consider the function $y=-\frac{1}{x}$y=−1x​

Medium
2min

Consider the function $y=\frac{2}{x}$y=2x​

Medium
1min

Consider the reciprocal function: $y=\frac{1}{x}$y=1x​

Medium
1min
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Outcomes

F.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.C.7.D (+)

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

F.BF.A.1.A

Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.A.1.B

Combine standard function types using arithmetic operations.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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