Download Unit 2 Answers 2.1 Introduction of and evaluating functions Practice

Unit 2 Answers
2.1 Introduction of and evaluating functions
Practice
Determine if each relation is a function.
1.
2.
3.
4.
5.
6.
7. {[6, -3), (7, 4), (-7, -2), (0, -2)}
8. {(7, 1), (7, -3), (7, 4)}
9.
x
y
10.
x
y
-3
1
1
3
0
1
2
2
0
11.
x
y
-4
-6
36
2
1
4
-4
-3
0
9
0
-2
3
3
9
Evaluate the function.
12. If f(x)=2x-3, find f(-2)
13. If f(x)=2x-3, find f(7)
14. If k(x)=-7x+1, find k(0)
15. If k(x)=-7x+1, find k(-1)
16. f(x)=2x-3 and f(x)=15, find the value of x.
Review Problems (complete ALL)
17. Solve for y: 5x-12y=24
!
18. Solve for x: 4x – 3(x+2)= -5x +2
19. solve for x: !! ≥ 5
20. ! + 4 = 12
21. Solve for x: 6x-2(x-2)=-3x+5
22. solve for y: 2x-3y=15
23. solve for x: ! − 5 = 10
2.2 Arithmetic Sequence
Practice
1. Find the 10th term of each of the following arithmetic sequences.
{19, 25, 31, 37 … }
{101, 97, 93, 89…}
2. Find the 15th term of each of the following arithmetic sequences.
{31, 36, 41, 46…}
{5, -3, -11, -19…}
3. Consider the sequence {87, 83, 79, 75…}
a. Show that the sequence is arithmetic (does it have a common difference?
What is the common difference?)
b. Find the explicit (general) form.
c. Find the recursive form.
d. Find the 40th term
e. Which term of the sequence is -297?
4. Consider the sequence {6, 17, 28, 39, 50…}
a. Show that the sequence is arithmetic.
b. Find the explicit (general) form.
c. Find the recursive form.
d. Find the 40th term
e. Which term of the sequence is 330?
5. Edgar is getting better at math. On his first quiz he scored 57 points, then he
scores 61 and 65 on his next two quizzes. If his scores continued to increase at the
same rate, what will be his score on his 9th quiz? Show all work.
a. Write an explicit formula for the sequence. Explain where you found the
numbers you are putting in the formula.
b. Identify the value of n and explain where you found it. Use the explicit
formula to solve the problem.
c. Write your final answer as a sentence.
6. Sherry works at the local fast food chain at the rate of $32.50/hr. The
management said that, depending on her performance, her hourly wage will be
increased by $7.50/hr every month. In how many months will she be receiving $85
an hour?
7. There is a stack of logs in the backyard. There are 15 logs in the 1st layer, 14 in the
second, 13 in the third, 12 in the fourth, and so on with the last layer having one
log. How many logs are in the stack?
8. Jerry deposited $20,000 on an investment that will give $1,750 for every year that
his money stays in the account. How much money will he have in his account by
the end of year 8?
Review Problems (complete ALL)
9. Evaluate the function f(x)=5(x+3)-2 given f(3).
!
10. Solve for y: 3x+4y=-16
11. Solve for m:
12. ! + 3 = −5
13. 2 ! + −4 = 10
14. 4-3(2x-5)=12x-3
15. -12x + 10 ≥ -10x+2
16. Determine if the function is a relation
then explain.
17. Determine if the function is a relation
then explain.
!
=2
2.3 Write, graph, & interpret equations (and word problems) given slope & y-intercept.
Practice
Graph each equation
!
1. ! = − ! ! + 2
2. 3! = 2! − 6
3. 6! + 3! = 6
4. Carla has already written 10 pages of a novel. She
plans to write 15 additional pages per month until she
is finished.
Write an equation to find the total number of pages P
written after any number of months, m.
Graph the equation on the grid.
Find the total number of pages written after 5 months.
Write an equation of the line that passes through the point and has the given slope.
5. (-4, 1) slope -1.
6. (2, 6) slope 2
!
7. (5, -3) slope !
Write an equation of the line that passes through each pair of points.
8. (9, -2), (4, 3)
9. (-5, 3), (0, -7)
10. (-1, -3), (-2, 3)
11. In 1904, a dictionary cost 30 cents. Since then the cost of a dictionary has risen an
average of 6 cents per year.
Write a linear equation to find the cost C of a dictionary y years after 1904.
If this trend continues, what will the cost of a dictionary be in 2020?
12. Jackson is ordering tickets for a concert online.
There is a processing fee for each order, and the
tickets are $52 each. Jackson ordered 5 tickets
and the cost was $275.
Determine the processing fee. Write a linear
equation to represent the total cost C for t tickets.
Make a table of values for at least three other
numbers of tickets.
Graph this equation. Predict the cost of 8 tickets.
13. A plumber charges $25 for a service call plus
$50 per hour of service. Write an equation in slope-intercept form for the cost, C,
after h hours of service. What will be the total cost for 8 hours of work? 10 hours of
work?
14. A caterer charges $120 to cater a party for 15 people and $200 for 25 people.
Assume that the cost, y, is a linear function of the number of x people. Write an
equation in slope-intercept form for this function. What does the slope represent?
How much would a party for 40 people cost?
15. Which equation best represents the graph?
a. ! = 2!
b. ! = −2!
!
c. ! = ! !
!
d. ! = − ! !
Review Problems (complete ALL)
!
16. Evaluate the function: f(x) = -!x + 5 when f(x) =-6
17. −3 ! + 2 − 7 ≤ 4(−! + 4)
!
19. If ℎ ! = ! ! − 3 find ℎ(6)
18. Solve for y: -4x+6y=-3
!
20. !! < 12
21. Consider the sequence {4, -2, -8, -14, -20,…}
a. Show that the sequence is arithmetic.
b. Find the explicit (general) form.
c. Find the recursive form.
e. Find the 29th term
e. Which term of the sequence is -98?
22. Determine if the relation is a function and explain why.
-5
6
3
-2
3
2
1
23. −2 2! + 4 = −12
24. Tori deposited $5,000 on an investment for college that will give $175 for every
year that her money stays in the account. How much money will 2he have in her
account by the end of year 12?
2.4 Write, graph, & interpret equations (and word problems) given two points.
Practice
Write an equation in point-slope form based on the given information. Then convert
the equation to slope-intercept form.
!
1. point: (-2, 5), slope: -6
2. point: (4, 3), slope: − !
3. points: (-1, 7), (8, -2)
4. points: (-4, 3), (0, 1)
!
5. point: (-6, -8), ! = − !
!
6. (-2, 11), ! = !
Write an equation in point-slope form to model each situation. Then re-write the
point-slope form to slope-intercept form.
7. The number of copies of a movie rented at a video kiosk decreased at a constant
rate of 5 copies per week. The 6th week after the movie was released, 4 copies were
rented. How many copies were rented during the second week?
8. Write an equation in point-slope form for the line
containing !". Write the slope-intercept form of
line.
the
9. The barometric pressure is 598 millimeters of mercury (mmHg) at an altitude of 1.8
kilometers and 577 millimeters of mercury at 2.1 kilometers. Write a formula for the
barometric pressure as a function of the altitude. What is the altitude if the pressure is
567 millimeters of mercury?
10. You bought 8 pencils for $3.35 on Monday. Your friend bought 10 pencils for $4.25
on Friday. Write an equation to model the total bill y, in dollars, for the number of
pencils, x.
11. At 7am I leave for school, which is 30 miles away. At 7:15am I am 18 miles away.
Write an equation in point-slope form to model this situation and then find the
distance I am away from the school after 25 minutes. (y is the distance away from
the school and x is the time)
12. Andrew is a submarine commander. He decides to surface his submarine to
periscope depth. It takes him 20 minutes to get from a depth of 400 feet to depth of
50 feet. Write an equation in point-slope form that describes this situation. What was
the submarine’s depth five minutes after it started surfacing?
Review Problems (complete ALL)
13. ! ! = 2! ! − 1 find f(3)
14. Is this a function? Explain why or
why not.
15. Timmy has 3, 000 miles on his car. He drives 38 miles each day. Write a linear
model to represent the situation. How many miles will he have on his car after 20
days?
x
y
-2
2
0
1
16. Given the points (-1, 5) & (3, 7)
-2
0
(a) Find the slope
1
-1
(b) Write the equation of the line.
2.5 Line of Fit and Extrapolation
Practice
Select the best line of fit for the data.
1.
! = −! + 4.5
2.
! = 10! + 20
!
! = 20! + 10
! = −!! + 4
For each of the following situations, calculate the regression line & correlation.
Interpret the slope and y-intercept in context of the problem and describe the
correlation. (You will complete the starred problems after the NEXT lesson)
3. The accompanying table shows the enrollment
a preschool from 1980 through 2000. (Remember,
order to interpret y-intercept we must use 0, 5, 10,
for years instead of 1980, 1985, etc.)
Linear Regression Equation:
M What does slope mean in this context?
M What does y-intercept mean in this context?
Correlation coefficient:
Describe correlation:
of
in
…
4. The accompanying table shows the percent of the
adult population that married before age 25 in
several different years.
Linear Regression Equation:
M What does slope mean in this context?
M What does y-intercept mean in this context?
Correlation coefficient:
Describe correlation:
Using the equation found above, estimate the percent of the adult population in the
year 2009 that will marry before age 25, and round to the nearest tenth of a percent.
5. A factory is producing and stockpiling metal
sheets to be shipped to an automobile
manufacturing plant. The factory ships only when
is a minimum of 2,050 sheets in stock. The
accompanying table shows the day, x, and the
number of sheets in stock, f(x).
there
Linear Regression Equation:
M What does slope mean in this context?
M What does y-intercept mean in this context?
Correlation coefficient:
Describe correlation:
Use this equation to determine the day the sheets will be shipped.
6. Since 1990, fireworks usage nationwide has grown, as shown in the accompanying
table, where t represents the number of years since 1990, and p represents the
fireworks usage per year, in millions of pounds.
Linear Regression Equation:
M What does slope mean in this context?
M What does y-intercept mean in this context?
Correlation coefficient:
Describe correlation:
Using this equation, determine in what year fireworks usage would have reached 99
million pounds.
Based on this linear model, how many millions of pounds of fireworks would be used in
the year 2008? Round your answer to the nearest tenth.
7. The accompanying table illustrates the number of movie theaters showing a
popular film and the film's weekly gross earnings, in millions of dollars.
Linear Regression Equation:
M What does slope mean in this context?
M What does y-intercept mean in this context?
Correlation coefficient:
Describe correlation:
Using this linear regression equation, find the approximate gross earnings, in millions of
dollars, generated by 610 theaters. Round your answer to two decimal places.
Find the minimum number of theaters that would generate at least 7.65 million dollars
in gross earnings in one week.
Review Problems (complete ALL)
8. Solve: 2(x-1) + 3x = 4x
9. Solve & graph : -2 ≤ 4x-2 ≤ 10
10. Is this a function? Explain why or why not.
{(2, 3), (4, 3), (5, 5)}
11. Find the explicit formula.
{-2, 3, 8, 13}
12. Write the equation of the line
with a slope of -2 that passes
through (1, -3).
13. Graph 3x-2y=10
2.6 Correlation or Causation & Interpreting Slope & Intercepts
Practice
1. Go back and answer all the starred questions in 2.5 (interpret slope & y=intercept,
including even #s)
3. Go back and find the x-intercept (substitute y=0 and solve for x) and interpret for
the odd # questions in 2.5
Identify the relationship between the two quantities in the given question as
causation or correlation.
4. The number of cold, snowy days and the amount of hot chocolate sold at a ski
resort.
5. The number of miles driven and the amount of gas used.
6. The number of additional calories consumed and the amount of weight gained.
7. The age of a child and his/her shoe size.
8. The amount of cars a salesperson sells and how much commission he makes.
9. The number of homework assignments turned in and how well and individual does
in class.
10. The annual salary and blood pressure for men ages 20-60.
11. The high divorce rate and lower death rates in the South.
Review Problems (complete ALL)
12. Solve: 3! − 2 + 1 = 13
14. Evaluate f(-2) if f(x) = -4x -7
13. Solve: -2x +5 ≤ 13
15. What is the 23rd term?
{(24, 21, 18, 15, …)}
Make sure you show the formula used to obtain the answer.
16. Write the equation of the line that passes through (-2, -4), and (4, 2).
17. Graph 2y=4x-6