Questions and Answers
Which graph represents a linear function?
Which statement best describes the relation (package number, price)?
It is not a function because each package number has two different prices.
Which answer explains whether the table of values represents a function?
Yes, the values represent a function because each x-value is paired with only one y-value.
Which relation is a function of x?
Signup and view all the answers
Why is Li incorrect in saying that the graph shows a direct variation?
Signup and view all the answers
Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?
Signup and view all the answers
A similar right triangle would be created by a rise of 8 and a run of?
Signup and view all the answers
Which equation represents a direct variation?
Signup and view all the answers
What does the function f(n + 1) = f(n) + 0.8 describe?
Signup and view all the answers
What is the value of a if a line passes through the points (2, -2) and (-6, 2) and the point (a, -4) is also on the line?
Signup and view all the answers
Does the amount of money in Sylvester's bank account represent a linear or non-linear function, and why?
Signup and view all the answers
Based on the graph, which relationship exists between the speed of the swing and the distance the ball travels?
Signup and view all the answers
Is the function in the graph non-linear?
Signup and view all the answers
Which representation represents a proportional relationship?
Signup and view all the answers
Which describes whether or not the line drawn through (-4, 3) and (4, 3) represents a direct variation?
Signup and view all the answers
Study Notes
Linear Functions and Relations
- A graph is classified as a linear function based on its representation, specifically graph B.
- Fun Zone party packages show prices that increase by $50 on weekends compared to weekdays, indicating that the relation between package numbers and prices is not a function due to multiple prices for the same package.
Functions and Tables
- A table of values represents a function when each x-value links to a unique y-value, confirming the requirement for function definition.
- Certain relations, like graph D, qualify as functions of x due to their characteristics.
Characteristics of Graphs and Direct Variation
- Li's claim about a graph depicting direct variation may be incorrect, implying a deeper understanding of direct relationships is necessary.
- The use of a straight line in figure C helps demonstrate that a graphed equation might not represent a function of x.
Geometric Relationships
- In right triangle ABC, a rising value of 8 with a run of 6 indicates dimensions of scaled similar triangles.
- The equation y=0.5x exemplifies direct variation, demonstrating the relationship where y varies directly with x.
Sequences and Growth
- The function representing snow depth f(n + 1) = f(n) + 0.8 shows an initial depth of 2.5 inches increasing by 0.8 inches hourly.
Application of Linear Functions
- A line intersecting points (2, -2) and (-6, 2) includes point (a, -4) with a calculated value of a as 6.
- The table of Sylvester's bank account indicates a non-linear function, as there’s no constant rate of change in account balance over time.
Relationships and Rates of Change
- The distance a baseball travels is directly proportional to the swing speed, with distance being five times the swing speed, showcasing direct variation in movement.
- A line that connects (-4, 3) and (4, 3) does not exemplify direct variation due to its failure to pass through the origin, negating the condition for direct proportionality.
Proportionality
- Specific representations (like graph D) can indicate proportional relationships, implying a consistent ratio between variables.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of linear functions with these flashcards. Each card presents a question or scenario that will challenge your understanding of the topic, including interpreting graphs and analyzing pricing models. Ideal for students preparing for assessments on linear functions.
