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2.2 Function Application (Due 10/18/22 SoC)

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Last updated 2 months ago
57 questions
Note from the author:
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Essential Question: What is function notation and what is it used for?

Learning Target: Students will be able to use function notation to evaluate functions that represent real-world functions.

Complete the entire assignment and show work for full credit.
Essential Question: What is function notation and what is it used for?

Learning Target: Students will be able to use function notation to evaluate functions that represent real-world functions.

Complete the entire assignment and show work for full credit.

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).

Question 1
1.

Complete the following notes regarding how to use function notation.

Question 2
2.

Evaluate each function for the given value.

Question 3
3.

Evaluate each function for the given value.

Question 4
4.

Evaluate each function for the given value.

Question 5
5.

Evaluate each function for the given value.

Question 6
6.

Evaluate each function for the given value.

For questions 8-11, use the functions to the left.

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10
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10
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10
Question 11
11.

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 10/11/22

Spiral Review

Question 12
12.

Question 13
13.

Question 14
14.

Directions: Complete each function table, then graph the function.


Question 15
15.

Directions: Complete each function table, then graph the function.


Triangle Problem: Consider the relationship between the number of triangles in each figure in the diagram below and the perimeter of each figure.

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20
Required
2
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2
A.REI.10
Required
2
Required
10
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2
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20

Day 3 10/14/22

Question 23
23.

Question 24
24.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

Question 25
25.

Question 26
26.

Question 27
27.

Question 28
28.

Question 29
29.

What is the graph of 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.

Question 30
30.

The function rule below represents the total weight W, in pounds, of a spa that contains g gallons of water. What is a reasonable graph of the function rule, given that the capacity of the spa is 250 gal?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.


Required
10
Question 31
31.

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. Enter only a number.


Question 32
32.

Graph the function rule.


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.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.


Question 33
33.

Question 34
34.

Day 4 10/17/22

Spiral Review

Question 35
35.

Translate this expression.

“eighteen less than a number”

Question 36
36.

Translate this expression.

“the difference of a number and 4"

Question 37
37.

Question 38
38.

Question 39
39.

Question 40
40.

Question 41
41.

Directions: Give the perimeter of each figure as a simplified expression.

Question 42
42.

Directions: Give the perimeter of each figure as a simplified expression.

Question 43
43.

Evaluate each expression using the variable replacements.


Evaluating Expressions

Question 44
44.

Evaluate each expression using the variable replacements.


Question 45
45.

Draggable itemarrow_right_altCorresponding Item
arrow_right_alt
arrow_right_alt
arrow_right_alt
arrow_right_alt
Question 46
46.

Question 47
47.

Question 48
48.

Solve this equation.


Question 49
49.

Question 50
50.

Question 51
51.

Solve this equation.


Question 52
52.

Solve this equation.

15h - 9 = - 54

Question 53
53.

Question 54
54.

Solve this multi-step equation. Show your work (SYW)

Question 55
55.

Solve this equation

Question 56
56.

Solve each proportion. Show your work! Or suffer the consequences...


Question 57
57.

Solve and graph the inequality for the given variable.

Question 7
7.

Evaluate each function for the given value.

Question 8
8.

Evaluate each function for the given value.

Question 9
9.

Evaluate each function for the given value.

Question 10
10.

Evaluate each function for the given value.

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
Classify each item on the left based on whether it describes the domain or range of a relation.
The y-values of a relation (usually)
Represented on the horizontal axis of a coordinate plane
The x-values of a relation (usually)
Represented on the vertical axis of a coordinate plane
The output values of a relation
The input values of a relation
Domain
Range
Question 16
16.

Triangle Problem:

Represent this relationship with a table and a graph.

Use contrasting colors to:
  1. Complete the table on the canvas.
  2. Plot the points on the coordinate plane
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Question 17
17.

Question 18
18.

Application Problem. Consider the relationship represented in the table below.

Question 19
19.

Question 20
20.

Application Problem:
Describe the relationship using words.

Question 21
21.

Question 22
22.

Application Problem:

Represent the relationship using a graph. Use contrasting colors. You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 1 Got It? Drag the values from the left to identify the domain and range of the relation.
Place each value only once.
4
-7
2
-2
-1
-4
1
7
Domain
Range
Vocabulary Review: A function is a relationship that pairs each input value with exactly one output value. Categorize each relationship.
Relation A
Relation C
Relation B
Function
Not a function
Vocabulary: Tell whether the relationship should be represented by a continuous or a discrete graph.

The amount of gas g remaining in the tank of a gas grill depends on the amount of time t the grill has been used.
continuous
discrete
Vocabulary: Tell whether the relationship should be represented by a continuous or a discrete graph.

The number of bagels b remaining in a dozen depends on the number s sold.
continuous
discrete
What is f(2) for the function f(x) = 4x + 1?
9
43
3
-2
Vocabulary: Is the graph for the function rule in the previous item continuous or discrete?
continuous
discrete
Vocabulary: Is the graph for the function rule in the previous item continuous or discrete?
continuous
discrete
Which words or phrases have the same meaning as addition?
total
how many groups of_____ are in_____
less than
together
product
multiply
increased by
more than
groups of
split
Which words or phrases have the same meaning as subtraction?
difference
the distance between
increased by
how many groups of_____ are in_____
decreased by
product
groups of
together
multiply
less than
___ groups of ___
Which words or phrases have the same meaning as division?
split in half
increased by
less than
minus
more than
product
put into four equal parts
how many groups of_____ are in_____
divide
multiply
total
Which words or phrases have the same meaning as multiplication?
plus
product
total
divide
times
more than
together
___ groups of ___
of
less than
minus
Match the operation with its inverse.
inverse of division
subtraction
inverse of multiplication
addition
inverse of addition
division
inverse of subtraction
multiplication
To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order.

Put these operations in the order by which you perform them to solve an equation. (first to last)
multiplication and division
parentheses ( )
addition and subtraction (outside parentheses)
Put the steps to solving this equation in the right order.
the result is x=7
Before we start solving, we identify the variable a, so we can solve for it the variable
divide both sides of the equation by 3
add 7 to both sides of the equation
What is the first step to solving this equation?

subtraction both sides of the equation by 3
multiplying both sides of the equation by 4
dividing both sides of the equation by 4
subtracting both sides of the equation by 11
What is the second step to solving this equation?

multiplying both sides of the equation by 4
dividing both sides of the equation by 4
subtracting both sides of the equation by 11
subtraction both sides of the equation by 3
Put the steps in the correct order to solve this multistep equation.


Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
Use distribution to multiply (7a+5) by -4 to get -28a - 20
undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
The solution is a = 5
Triangle Problem:

Which equation represents the relationship?
p=14t+2
p=14t
p=4t+6
p=6t+4
Triangle Problem:

Suppose you know the perimeter of n triangles. What would you do to find the perimeter of n + 1 triangles?
Add 5 to the perimeter of n triangles.
Add 2 to the perimeter of n triangles.
Add 4 to the perimeter of n triangles.
Add 3 to the perimeter of n triangles.
Application Problem:

Does the relationship represent a linear function?
No
Yes
Application Problem:

Which equation represents the relationship?
y=x+9
y=8x+1
y=2x+8
y=x+8