Podcast
Questions and Answers
Express the relation {(7, 5), (8, -2), (7, 6), (-4, -9), (0, -2)} as a table and a mapping diagram.
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.
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?
B) Is the relation a function?
False (B)
For the following relation, determine the domain and range. Tell whether the relation is a function.
For the following relation, determine the domain and range. Tell whether the relation is a function.
Determine if each relation is a function.
Determine if each relation is a function.
The more time you spend studying, the better your grade will be on your quiz.
Independent:
Dependent:
The more time you spend studying, the better your grade will be on your quiz. Independent: Dependent:
The faster you drive, the quicker you will arrive at your destination.
Independent:
Dependent:
The faster you drive, the quicker you will arrive at your destination. Independent: Dependent:
A) f(-8) =
A) f(-8) =
D) find x if f(x) = 6
D) find x if f(x) = 6
H(3)
H(3)
F(2) + h(-5)
F(2) + h(-5)
H(0) - f(1)
H(0) - f(1)
Find x if f(x) = -31
Find x if f(x) = -31
Solve for y in each equation. Write y on the left side.
2x - 6y = 8
Solve for y in each equation. Write y on the left side. 2x - 6y = 8
Make a table and graph.
4y = 4x + 8, D = {-8, -4, 0, 4, 8}
Make a table and graph. 4y = 4x + 8, D = {-8, -4, 0, 4, 8}
Make a table and graph.
y + 3 = x² + 5
Make a table and graph. y + 3 = x² + 5
Flashcards
Relation
Relation
A set of ordered pairs (x, y).
Function
Function
A relation where each input (x) has only one output (y).
Domain
Domain
The set of all possible input values (x) in a relation or function.
Range
Range
Signup and view all the flashcards
Independent Variable
Independent Variable
Signup and view all the flashcards
Dependent Variable
Dependent Variable
Signup and view all the flashcards
𝑓(𝑥)
𝑓(𝑥)
Signup and view all the flashcards
𝑓(−8)
𝑓(−8)
Signup and view all the flashcards
𝑓(8)
𝑓(8)
Signup and view all the flashcards
𝑥 if 𝑓(𝑥)=6
𝑥 if 𝑓(𝑥)=6
Signup and view all the flashcards
Solve for y
Solve for y
Signup and view all the flashcards
𝑓(2)+ℎ(-5)
𝑓(2)+ℎ(-5)
Signup and view all the flashcards
ℎ(0) − 𝑓(1)
ℎ(0) − 𝑓(1)
Signup and view all the flashcards
𝑥 if 𝑓(𝑥) = -31
𝑥 if 𝑓(𝑥) = -31
Signup and view all the flashcards
Mapping diagram
Mapping diagram
Signup and view all the flashcards
Ordered pairs
Ordered pairs
Signup and view all the flashcards
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.)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
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!
