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6.01 Rational functions

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

AII.6b

For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions use knowledge of transformations to convert between equations and the corresponding graphs of functions

AII.7a

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of domain, range and continuity

AII.7b

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of intervals in which a function is increasing or decreasing

AII.7c

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of extrema

AII.7d

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of zeros

AII.7e

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of intercepts

AII.7f

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of values of a function for elements in its domain

AII.7g

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs

AII.7h

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of end behaviour

AII.7i

Investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically for the concept of vertical and horizontal asymptotes

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