6.03 Identifying functions
Express the relation \left\{\left(2, 2\right), \left(4, 4\right), \left(6, 3\right), \left(7, 5\right)\right\} in a table of values.
Express the relation \left\{\left(1, 2\right), \left(3, 5\right), \left(7, 8\right), \left(8, 11\right)\right\} as a series of points on the coordinate plane.
Determine whether the following statements are true or false:
When working with a function, substituting a certain value of x into the formula gives only one value of y for that value of x.
All relations are functions.
Some relations are functions.
All functions are relations.
No functions are relations.
No relations are functions.
A relation always passes the vertical line test.
The graph of every straight line is a function.
The graph of every non-vertical straight line is a function.
There is no straight line graph that is a function.
The graph of every straight line is a relation.
The graph of every non-horizontal straight line is a function.
Identify the name used to describe a graph where for some value of x, there exists two or more different values of y.
Classify the following sets of points as a relation or a function:
\left\{\left(2, 5\right), \left(7, - 3 \right), \left(5, 2\right), \left( - 4 , - 9 \right)\right\}
\left\{\left(2, 5\right), \left(2, 7\right), \left( - 3 , - 4 \right), \left( - 9 , 13\right)\right\}
\left\{\left(1, 5\right), \left(1, 1\right), \left(7, - 2 \right), \left( - 5 , - 10 \right)\right\}
\left\{\left(1, 5\right), \left(7, - 2 \right), \left( - 5 , - 10 \right), \left(13, - 13 \right)\right\}
\left\{\left(1, 5\right), \left(1, 7\right), \left( - 2 , - 5 \right), \left( - 5 , - 10 \right)\right\}
\left\{\left(-1, -9\right), \left(0, 0\right), \left(1 , 9 \right), \left( 2, 18 \right)\right\}
\left\{\left(-2, 4\right), \left(-1, 1\right), \left(2,4\right), \left( 6, 36 \right)\right\}
\left\{\left(0, 0\right), \left(1, \dfrac{1}{3}\right), \left(2,\dfrac{2}{3}\right), \left( 3, 1 \right)\right\}
The pairs of values in the table represent a relation between x and y. Determine whether they represent a function:
| x | - 4 | - 3 | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| y | - 4 | - 3 | - 2 | -1 | 0 | -1 | - 2 | - 3 | - 4 |
| x | 0 | 1 | 4 | 8 | 9 | 12 | 16 | 18 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 2 \sqrt{2} | 3 | 2 \sqrt{3} | 4 | 3 \sqrt{2} | 2 \sqrt{5} |
| x | - 9 | - 7 | - 6 | - 5 | - 3 | - 2 | 3 | 5 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| y | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
| x | - 8 | - 7 | - 6 | - 3 | 2 | 7 | 9 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| y | 8 | 13 | - 18 | - 16 | - 15 | - 2 | - 4 | 11 | - 9 |
Consider the points in the table:
| x | - 4 | - 3 | 0 | - 1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| y | 4 | 3 | 2 | 1 | 0 | 1 | 2 | 3 | 4 |
Plot the points on a coordinate plane.
Do they represent a function?
A relation is defined as follows:
y = 1 if x is positive and y = -1 if x is 0 or negative.
Complete the table for this relation:
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| y |
Plot the points on a coordinate plane.
Do these values represent a function?
The following sets of points represent a relation between x and y. Find a value of k such that the relation does not represent a function:
Consider the following ordered pairs:
\left\{\left( - 9 , - 5 \right), \left( - 5 , - 10 \right), \left( - 5 , - 4 \right), \left( - 3 , 7\right), \left( - 2 , - 4 \right), \left( - 1 , 1\right)\right\}
Plot the ordered pairs on a coordinate plane.
Which ordered pair would need to be removed from the set so that the remaining ordered pairs represent a function?
Crazy Mobile charges \$2.80 a minute plus a connection fee of 90\text{c} for an international call.
Complete the table.
Is this relation a function?
| Call length (minutes) | International call cost (dollars) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
A particular store is offering one free T-shirt for every two T-shirts purchased, where each T-shirt costs \$19.
Complete the table.
Is this relation a function?
| Number of T-shirts | Total cost (dollars) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
A particular internet service provider charges \$40 a month on their 20 \text{ GB} plan and charges \$10 for each additional 10 \text{ GB} used.
Complete the table.
Is this relation a function?
| Total GB used | Total charge (dollars) |
|---|---|
| 10 | |
| 20 | |
| 30 | |
| 40 | |
| 50 |
Tracy makes scarfs to sell at the market. It costs her \$3 to produce each one, and she sells them for \$6.
Consider when 1, 2, 3, 4 and 5 scarfs are sold. Plot the points representing the relation between the number of scarfs she manages to sell and her total profit.
State whether the relation is a function.