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Common Core Math I
Unit 3 – Functions Review
I.State whether each set is a function. Answer yes or no. Find the domain and the range.
1){(4, 3), (-2, 10), (4, -6), (10, 7)}Domain:Range:
2){(-3, -6), (-8, -6), (-1, 2), (3, 0)}Domain:Range:
Use the vertical line test to determine whether each graph is the graph of a function. Answer yes or no.
3) 4) 5)
Use and to find each value.
6)7)8)9)
10)Jeff is printing flyers for his car wash. The copy store will charge $3.00 the initial printing, and $.05 for each copy where c is the number of copies and P is the total price. This is modeled by Evaluate
and find the meaning.
II.Functions
Determine if the following ordered pairs are solutions of the given equations.
1) 2)
III.1)2)
x / 0 / 1 / 2 / 3 / 4y / 4 / 12 / 20 / 28 / 36
x / 0 / 1 / 2 / 3 / 4
y / 3 / 15 / 75 / 375 / 1875
(a) NEXT= starting at (a)NEXT= starting at
(b)(b)
(c) Find y if .(c) Find y if .
3)Jim is timing the rate of a chemical reaction. Let t be the number of minutes the reaction is taking. Let r be the reaction speed in L/min.
Minutes t / 0 / 1 / 2 / 3 / 4Reaction Speed r () / 6 / 9 / 12
(a) Complete the table.
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(b)Write a NOW-NEXT showing how the reaction changes from one month to the next.
(c)Describe the pattern in the values (arithmetic or geometric).
(d)Write an explicit equation for this process (a equation).
(e)What will the speed of the reaction be after 22 minutes?
(f)When will the reaction have a speed of 80 L/min?
4)Grant has $58 in a savings account. He plans on depositing $30 into the account each month and not taking any money out of the account. Which function rule will give the total amount he has in the account T after any number of months n?
5)The graph below indicates the value of a small used car as a function of how old the car is.
a. Estimate the slope and y-intercept of the line. Explain how you made each estimate.
Estimate of the slope: ______
Explanation:
Estimate of the y-intercept: ______
Explanation:
b. Write a function rule that would match the graph.
Function rule: ______
c. Explain the meaning of the line in terms of the value of the car and the age of the car.
6)Michelle participated in a walk for charity. Her mother donated $5 and then gave an additional $2 for each mile that Michelle completed during the 3-hour walk.
a. Complete the table below to indicate how much Michelle’s mother owed as a function of the distance Michelle walked.
b. Write a rule relating NOW and NEXT that shows how the amount Michelle’s mother owed
changed with each additional mile that Michelle walked.
NEXT = ______, starting at ______
7)Use the words NOW and NEXT to write rules that match each table below. Explain your reasoning.
a.
NEXT = ______, starting at ______
b.
NEXT = ______, starting at ______
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IV.Jessica was driving to school, but forgot something, so she turned around and went back home to get it. The graph below models her path where time t is given in minutes and Distance from home D is given in miles.
1)What is the independent variable?
2)What is the dependent variable?
3)What is the domain? What kind of numbers would
you possibly have?
4)What is the range? What kind of numbers would
you possibly have?
5)What does?
6)What doesmean in words?
7)Find the rate of change of Jessica’s path over the first three min.
8)Explain the meaning of the rate of change you found in #7.
9)Find the value of the x-intercept(s). 10) Explain the meaning of the x-intercept.
11)Find the value of the y-intercept.12)Explain the meaning of the y-intercept.
13)What was Jessica’s maximum distance from home? At what time did she reach this distance?
14)What is the meaning of this maximum?
16)What was Jessica’s minimum distance from home? At what time(s) did she reach this distance?
17)What is the meaning of this (these) minimum(s)?
18)What happened at
19)When was Jessica’s distance increasing? What does this mean in the context of the problem?
20)When was Jessica’s distance decreasing? What does this mean in the context of the problem?