Topics
4. Rational Functions & Expressions
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United States of AmericaFL
Grade 912

4.05 Graphing the reciprocal function

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
Easy
2min

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

Easy
2min

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

Easy
1min

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

Easy
1min
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Outcomes

MA.912.AR.8.2

Given a table, equation or written description of a rational function, graph that function and determine its key features.

MA.912.AR.8.3

Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context.

MA.912.F.1.1

Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.

MA.912.F.2.2

Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y- values or multiplying the x- or y- values by a real number.

MA.912.F.2.3

Given the graph or table of f(x) and the graph or table of f(x)+k,kf(x), f(kx) and f(x+k), state the type of transformation and find the value of the real number k.

MA.912.F.2.5

Given a table, equation or graph that represents a function, create a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.

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