For each of the following pairs of variables:
State the independent variable.
State the dependent variable.
Number of ice cream cones sold and temperature outside.
Size of a pizza and cost of a pizza.
Time spent studying and exam mark.
Consider the function y=4x-3. Identify the following:
The independent variable
The dependent variable
State whether the following statements about functions are true or false:
When working with a function, substituting a certain value of x into the formula gives only 1 value of y for that value of x.
A horizontal line can intersect the graph of a function at more than one point.
A relation always passes the vertical line test.
All functions are relations.
All relations are functions.
Are all straight lines functions? Explain your answer.
Determine whether the following relations are functions:
Determine whether the following sets of points describe 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\}
Find a value of k such that the relation \left\{\left(6, 2\right), \left(8, 5\right), \left(1, 7\right), \left(k, 4\right)\right\} does not represent a function.
The pairs of values in the following tables 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 |
Consider the number of quarters in x years.
Complete the table:
Is this relation a function?
| \text{Years, }x | \text{Quarters} |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
For each of the following graphs, state the type of relation it is from the following:
One-to-one
Many-to-one
One-to-many
Many-to-many
Complete the statement: "A one-to-one function is a function in which ..."
Is a horizontal line a one-to-one function? Explain your answer.
A relation is defined as: 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 the number plane.
Do these values 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 the number plane.
Which ordered pair would need to be removed from the set so that the remaining ordered pairs represent a function?
Determine if the following graphs are one-to-one functions: