Essential Question: How can functions be used to model real-world relationships and solve problems in everyday situations?
Learning Target: Students will be able to apply functions to represent relationships between variables and use them to solve problems in various contexts, such as finding outputs for given inputs, interpreting graphs, and understanding how changes in one variable affect another.
Show your work for credit.
Day 1 10/21/24
Warm-up: Spiral Review
Required
8 points
8
Question 1
1.
Categorize each representation of a relation on the left based on its type.
\{(3,-9),(11,21),(121,34),(34,1)\}
Ordered Pairs
Mapping Diagram
Table of Values
Graph
Required
12 points
12
Question 2
2.
Classify each item on the left based on whether it describes the domain or range of a relation.
The input values of a relation
The output values of a relation
The x-values of a relation (usually)
Represented on the vertical axis of a coordinate plane
The y-values of a relation (usually)
Represented on the horizontal axis of a coordinate plane
Domain
Range
Required
20 points
20
Question 3
3.
Directions: Complete each function table, then graph the function.
Required
20 points
20
Question 4
4.
Directions: Complete each function table, then graph the function.
Required
10 points
10
Question 5
5.
Solve this multi-step equation. Show your work (SYW)
Main Idea: Functions and Function Notation
Throughout mathematics, we find function notation. Function notation is a way to write functions that is easy to read and understand. Functions have dependent and independent variables, and when we use function notation the independent variable is commonly x, and the dependent variable is f(x).
Required
30 points
30
Question 6
6.
Complete the following notes regarding how to use function notation.
Required
10 points
10
Question 7
7.
Evaluate each function for the given value.
Required
10 points
10
Question 8
8.
Evaluate each function for the given value.
Required
10 points
10
Question 9
9.
Evaluate each function for the given value.
Required
10 points
10
Question 10
10.
Evaluate each function for the given value.
Required
10 points
10
Question 11
11.
Evaluate each function for the given value.
For questions 8-11, use the functions to the left.
Required
10 points
10
Question 12
12.
Evaluate each function for the given value.
Required
10 points
10
Question 13
13.
Evaluate each function for the given value.
Required
10 points
10
Question 14
14.
Evaluate each function for the given value.
Required
10 points
10
Question 15
15.
Evaluate each function for the given value.
Required
10 points
10
Question 16
16.
Anthropologists use the length of certain bones of the human skeleton to estimate the height of the living person. One of these bones is the femur. To estimate the height in centimeters of a female with a femur length of x, the function h(x) = 61.41 + 2.32x can be used. If a 46 cm femur bone is discovered at a dig site, using the height function, estimate how tall the person was that bone belonged to.
Day 2 10/22/24
Warm-up: Spiral Review
Required
10 points
10
Question 17
17.
Drag the values from the left to identify the domain and range of the relation.
Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.
Required
5 points
5
Question 19
19.
Translate this expression.
“eighteen less than a number”
Required
8 points
8
Question 20
20.
Which words or phrases have the same meaning as addition?
Required
8 points
8
Question 21
21.
Which words or phrases have the same meaning as subtraction?
Required
8 points
8
Question 22
22.
Which words or phrases have the same meaning as division?
Required
8 points
8
Question 23
23.
Which words or phrases have the same meaning as multiplication?
Required
10 points
10
Question 24
24.
Solve this equation
Required
10 points
10
Question 25
25.
Solve each proportion.
Required
10 points
10
Question 26
26.
Solve and graph the inequality for the given variable.
Main Idea: Evaluating Expressions
Required
10 points
10
Question 27
27.
Evaluate each expression using the variable replacements.
Required
5 points
5
Question 28
28.
Evaluate each expression using the variable replacements.
10 points
10
Question 29
29.
Directions: Give the perimeter of each figure as a simplified expression.
_______
Now find the actual perimeter if y=13 meters
_______
Finally, find the area if y=7 meters
_______
10 points
10
Question 30
30.
Directions: Give the perimeter of each figure as a simplified expression.
_______
Now find the actual perimeter if y=8 meters
_______
Main Idea: Application of Functions
Required
20 points
20
Question 31
31.
The amount of water w in a wading pool, in gallons, depends on the amount of time t, in minutes, the wading pool has been filling, as related by the function rule w = 3t.
1) Graph the function rule.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.
2) If the pool can hold 70 gallons, how long would it take to fill it.
_______
Required
20 points
20
Question 32
32.
Use the function w(x) = 250x, which represents the average number of words a person can read in one minute to determine many words the average person can read in 6 minutes.
_______
Using w(x)=250x, how many minutes would it take to read the first Harry Potter book if the it has 76944 words?
