Podcast
Questions and Answers
I need help understanding the concept of a function as a rule or interpreting the graph of a function as a set of ordered pairs.
I need help understanding the concept of a function as a rule or interpreting the graph of a function as a set of ordered pairs.
False (B)
I can describe the qualitative features of a function from a graph most of the time.
I can describe the qualitative features of a function from a graph most of the time.
True (A)
I can identify basic properties of a single function with guidance.
I can identify basic properties of a single function with guidance.
True (A)
I need help comparing properties of two functions represented in different ways.
I need help comparing properties of two functions represented in different ways.
I can identify linear equations in the form with guidance. I need help interpreting the equation as defining a linear function or providing examples of nonlinear functions.
I can identify linear equations in the form with guidance. I need help interpreting the equation as defining a linear function or providing examples of nonlinear functions.
I can accurately describe the qualitative features of a function from a graph and sketch a graph that matches a verbal description.
I can accurately describe the qualitative features of a function from a graph and sketch a graph that matches a verbal description.
I can clearly explain the relationship between quantities and justify my reasoning.
I can clearly explain the relationship between quantities and justify my reasoning.
Is input 'any person' and output 'the month the person was born in' a function?
Is input 'any person' and output 'the month the person was born in' a function?
Is (2, 3), (0, 1), (2, -4), (3, -1), (2,4) a function?
Is (2, 3), (0, 1), (2, -4), (3, -1), (2,4) a function?
Is the 'Earnings of Manager B' graph a function?
Is the 'Earnings of Manager B' graph a function?
Is the Day/Temperature graph a function?
Is the Day/Temperature graph a function?
Is the Input/Output Table on the left a function?
Is the Input/Output Table on the left a function?
Is the equation $y = -2x + 5$ a function?
Is the equation $y = -2x + 5$ a function?
Is the equation $x = 4$ a function?
Is the equation $x = 4$ a function?
Which graph shows a nonlinear function and why?
Which graph shows a nonlinear function and why?
Given the linear function $y = 3x - 5$, find y when x = 2
Given the linear function $y = 3x - 5$, find y when x = 2
Given the linear function $y = 3x - 5$, find the output when the input is 3
Given the linear function $y = 3x - 5$, find the output when the input is 3
Given the linear function $y = 3x - 5$, find the value of the dependent variable when the independent variable is -4
Given the linear function $y = 3x - 5$, find the value of the dependent variable when the independent variable is -4
How much does A Plus Plumbing cost for each hour of work?
How much does A Plus Plumbing cost for each hour of work?
What is the one-time fee for A Plus Plumbing?
What is the one-time fee for A Plus Plumbing?
How much does Quality Plumbing charge for each hour of work?
How much does Quality Plumbing charge for each hour of work?
What is the one-time fee for Quality Plumbing?
What is the one-time fee for Quality Plumbing?
Can A Plus Plumbing and Quality Plumbing ever charge the same total for the same amount of time?
Can A Plus Plumbing and Quality Plumbing ever charge the same total for the same amount of time?
I can identify linear relationships and basic components of a function (e.g., slope and y-intercept) with guidance.
I can identify linear relationships and basic components of a function (e.g., slope and y-intercept) with guidance.
I need help constructing a function or interpreting the rate of change and initial value in context.
I need help constructing a function or interpreting the rate of change and initial value in context.
I can identify basic features of a graph with guidance.
I can identify basic features of a graph with guidance.
I need help describing the relationship between quantities or sketching a graph based on a verbal description.
I need help describing the relationship between quantities or sketching a graph based on a verbal description.
I can construct a function to model a linear relationship and determine the rate of change and initial value from a description, table, or graph most of the time.
I can construct a function to model a linear relationship and determine the rate of change and initial value from a description, table, or graph most of the time.
I can sketch a graph based on a verbal description but may make small errors.
I can sketch a graph based on a verbal description but may make small errors.
I can accurately construct a function to model a linear relationship and determine the rate of change and initial value from various representations.
I can accurately construct a function to model a linear relationship and determine the rate of change and initial value from various representations.
I can clearly interpret these values in context and explain my reasoning.
I can clearly interpret these values in context and explain my reasoning.
What is the slope of the line $y = -3/2x + 3$?
What is the slope of the line $y = -3/2x + 3$?
What is the y-intercept of the line $y = -3/2x + 3$?
What is the y-intercept of the line $y = -3/2x + 3$?
Is a linear function a straight line with only one output?
Is a linear function a straight line with only one output?
After how many weeks will the puppy weigh 33 pounds for the linear function $y = 3/2x + 3$?
After how many weeks will the puppy weigh 33 pounds for the linear function $y = 3/2x + 3$?
Write the slope of the first piece of the graph?
Write the slope of the first piece of the graph?
Write the slope of the second piece of the graph?
Write the slope of the second piece of the graph?
Write the y-intercept of the first piece of the graph?
Write the y-intercept of the first piece of the graph?
Write the y-intercept of the second piece of the graph?
Write the y-intercept of the second piece of the graph?
Write an equation for the first piece of the graph?
Write an equation for the first piece of the graph?
Write an equation for the second piece of the graph?
Write an equation for the second piece of the graph?
What does the slope of the first line segment represent in context?
What does the slope of the first line segment represent in context?
What does the slope of the second line segment represent in context?
What does the slope of the second line segment represent in context?
Flashcards
What is a Function?
What is a Function?
A relationship where each input has only one output.
What is a Linear Function?
What is a Linear Function?
A function represented by straight line equation in which for each input there is only one output.
What is a Nonlinear Function?
What is a Nonlinear Function?
A function that does not form a straight line when graphed, indicating the rate of change is not constant.
What is Slope?
What is Slope?
Signup and view all the flashcards
What is a y-intercept?
What is a y-intercept?
Signup and view all the flashcards
Study Notes
- This is Math 8 Formative Assessment 1 covering Unit 5 Functions and Volume.
Defining Functions
- A function is a rule where each input has only one output.
- Can be represented as graphs, tables, equations, or verbal descriptions.
- To determine if a relationship is a function, check that each input (x-value) has only one output (y-value).
- Vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.
Evaluating Functions
- Given a function, you can find the output (y) for any input (x) by substituting x into the equation.
- For f(x) = 3x - 5:
- If x = 2, then f(2) = 3(2) - 5 = 1.
- If f(x) = 7, then 7 = 3x - 5, so x = 4.
Comparing Functions
- Linear functions have a constant rate of change (slope) and can be written in the form y = mx + b.
- The slope (m) represents the rate of change (change in y over change in x).
- The y-intercept (b) represents the initial value or starting point (value of y when x = 0).
Modeling Relationships with Functions
- Can model real-world relationships using functions.
- For example, the cost of a plumbing service can be modeled as a linear function of time (hours).
- Need to determine the rate of change (slope) and initial value (y-intercept) from the given information (table, graph, or description).
Graphing Functions: Andre's Distance
- Andre's distance from the starting point as a function of time:
- Ran forward 20 yards.
- Then ran back 5 yards.
- Stood there for 3 seconds.
- Walked back to the starting point.
- The graph should have the axes labeled (distance in yards vs. time in seconds) and key points identified.
Linear Functions and Piecewise Functions
- Given a table of values, identify the linear function that relates the variables (e.g., weight of a puppy vs. age in weeks).
- Find the slope and y-intercept from the table.
- Write the equation in the form y = mx + b.
- Interpret the slope and y-intercept:
- Slope represents the rate of change (e.g., weight increase per week).
- Y-intercept represents the initial value (e.g., weight at birth).
- Determine the value after a number of weeks.
Piecewise Functions
- A piecewise function consists of different linear pieces over different intervals.
Variables Explained
- In a graph showing a relationship between two variables, identify the dependent and independent variables.
- The dependent variable is the output and depends on the independent variable (input).
- Create a story or real-world context for the relationship shown in the graph.
- A table and a piecewise function:
- The domain is the interval of x-values for each piece.
- The slope is the rate of change for each piece.
- The y-intercept is the value of y when x = 0.
- Write the equation for each piece in the form y = mx + b.
- Calculate the value of y at a specific x-value using the appropriate equation.
- Write the piecewise function by specifying the equation and domain for each piece.
- Contextualize the slope:
- Relate the slope of each line segment to the story or real-world context.
- Determine if each line represents saving or spending money.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
