Relations
Grab a warm-up off the wooden desk...
Goals:
Warm-Up #1
Write the coordinates of each point and name the quadrant or axis where the point is located.
Warm-up #1
Graph each of the given parent functions.
Warm-up #2
What comes First?
When one quantity depends on another in a situation, it is said to be the _________________ ______________. The quantity it depends upon is called the __________________ _______________.
Consider the two quantities that are changing in the relationship below.
The number of movie tickets purchased and the total cost.
What comes first?
Identify the Independent Quantity
Ask yourself: “What comes first?”
The number of eggs used and the number of cakes baked
Identify the Independent Quantity
Ask yourself: “What comes first?”
The number of students in attendance at school and the number of lunches served.
Identify the Independent Quantity
Ask yourself: “What comes first?”
The number of hours driven and the number of miles to a vacation destination.
Identify the Independent Quantity
Ask yourself: “What comes first?”
The number of minutes a swimming pool is filled with water and the number of gallons of water in the swimming pool.
Think-Pair-Share
Identifying Graphical Behaviors
Matthew grouped these graphs together. Why do you think Matthew put these graphs in the same group?
TPS:
Identifying Graphical Behaviors
Why might Clara have grouped these graphs together?
Think-Pair-Share:
Identifying Graphical Behaviors
Dylan grouped these graphs together because each graph goes through only two quadrants.
Explain why his reasoning is not correct.
Identifying Graphical Behaviors
Alyssa grouped these graphs together, but did not provide any rationale.
What do you notice about the graphs?
Why might they be grouped together?
Desmos: Graphing Stories
Tell me What you Learned Today!
Resources
Mod 1 Standards
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.�B. Focus on linear, quadratic, and exponential functions
F.BF.1 Write a function that describes a relationship between two quantities.�A. Determine an explicit expression, a recursive process, or steps for calculation from context. �I. Focus on linear and exponential functions�II. Focus on situations that exhibit quadratic or exponential relationships.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.