Relations and Functions Test Review

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Questions and Answers

Express the relation {(7, 5), (8, -2), (7, 6), (-4, -9), (0, -2)} as a table and a mapping diagram.

Table:

x	y
7	5
8	-2
7	6
-4	-9
0	-2

Mapping Diagram:

[Diagram showing the relationship between the x and y values, with arrows connecting them.]

A) Identify the domain and range of the relation.

Domain: {7, 8, -4, 0} Range: {5, -2, 6, -9}

B) Is the relation a function?

False

For the following relation, determine the domain and range. Tell whether the relation is a function.

<p>Domain: {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5} Range: {-1, 0, 1, 2, 3, 4, 5, 6, 7} Is the relation a function? Yes</p> Signup and view all the answers

Determine if each relation is a function.

<p>Yes</p> Signup and view all the answers

The more time you spend studying, the better your grade will be on your quiz. Independent: Dependent:

<p>Independent: Time spent studying Dependent: Grade on the quiz</p> Signup and view all the answers

The faster you drive, the quicker you will arrive at your destination. Independent: Dependent:

<p>Independent: Speed of driving Dependent: Time to arrive at destination</p> Signup and view all the answers

A) f(-8) =

<p>-11</p> Signup and view all the answers

D) find x if f(x) = 6

<p>x = 4.5</p> Signup and view all the answers

H(3)

<p>-12</p> Signup and view all the answers

F(2) + h(-5)

<p>19</p> Signup and view all the answers

H(0) - f(1)

<p>-5</p> Signup and view all the answers

Find x if f(x) = -31

<p>x = -17</p> Signup and view all the answers

Solve for y in each equation. Write y on the left side. 2x - 6y = 8

<p>y = (1/3)x - (4/3)</p> Signup and view all the answers

Make a table and graph. 4y = 4x + 8, D = {-8, -4, 0, 4, 8}

<p>Table:</p> <table> <thead> <tr> <th>x</th> <th>y</th> </tr> </thead> <tbody> <tr> <td>-8</td> <td>-6</td> </tr> <tr> <td>-4</td> <td>-2</td> </tr> <tr> <td>0</td> <td>2</td> </tr> <tr> <td>4</td> <td>6</td> </tr> <tr> <td>8</td> <td>10</td> </tr> </tbody> </table> <p>Graph:</p> <p>[Plot the points from the table on a coordinate plane, with x on the horizontal axis and y on the vertical axis. Draw a line connecting the points.]</p> Signup and view all the answers

Make a table and graph. y + 3 = x² + 5

<p>Table:</p> <table> <thead> <tr> <th>x</th> <th>y</th> </tr> </thead> <tbody> <tr> <td>-8</td> <td>61</td> </tr> <tr> <td>-4</td> <td>21</td> </tr> <tr> <td>0</td> <td>2</td> </tr> <tr> <td>4</td> <td>21</td> </tr> <tr> <td>8</td> <td>61</td> </tr> </tbody> </table> <p>Graph:</p> <p>[Plot the points from the table on a coordinate plane, with x on the horizontal axis and y on the vertical axis. Draw a curve connecting the points.]</p> Signup and view all the answers

Study Notes

Relations and Functions Test Review

Relation Representation: Relations can be expressed as ordered pairs, tables, or mapping diagrams. Example: {(7, 5), (8, -2), (7, 6), (-4, -9), (0, -2)}
Domain: The set of all input values (x-values) in a relation.
- Example: For the relation {(7, 5), (8, -2), (7, 6), (-4, -9), (0, -2)}, the domain is {7, 8, -4, 0}.
Range: The set of all output values (y-values) in a relation.
- Example: For the relation {(7, 5), (8, -2), (7, 6), (-4, -9), (0, -2)}, the range is {5, -2, 6, -9, -2}.
Function Definition: A relation where each input value (x-value) corresponds to exactly one output value (y-value).
Vertical Line Test: A graph represents a function if any vertical line drawn on the graph intersects the graph at most once.
Independent Variable: The variable whose value is being directly manipulated or controlled in an experiment. In the context of the problem, it represents the input.
Dependent Variable: The variable that is expected to change in response to the independent variable. In the context of the problem, it represents the output.
Evaluating Functions: Finding the output value (y-value) corresponding to a given input value (x-value) using a function rule or graph.

Solving Equations

Solve for y (isolate y): To solve an equation for y, rearrange the equation so that y is alone on one side.
- Example: For 2x - 6y = 8, to isolate y, first subtract 2x from both sides: -6y = -2x + 8. Then divide both sides by -6: y = (1/3)x - (4/3).
Linear Equations: Equations that can be graphed as straight lines.
Graphing Linear Equations: To graph a linear equation, you can find at least two points that satisfy the equation and connect them to form a line.

Functions by Graph, Table, and Mapping Diagrams

Example Problems: Several examples were given to identify if the relations are functions.

Additional function problems

Function notation: f(x) = output of the function when the input is x
- Example: f(2) represents the output when x equals 2 in the function f(x).
Finding values:
- Find f(x) = number. This means finding what x equals given the output value.
- Find f(x) = -31 (example).
- Find f in a variety of forms (graphs, functions etc.)

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Description

This quiz covers the key concepts of relations and functions, including how to represent relations, identify domains and ranges, and the definition of a function. You will also learn about the vertical line test and independent variables. Perfect for students preparing for their math assessments!