Every Saturday, Justin gets an allowance of $10 from his parents. During every week since Justin began getting an allowance, he spends $8 and saves the remaining $2 of his allowance before he receives his next allowance. The sequence shown represents the amount of money Justin has right before and right after he gets his allowance for six consecutive weeks, starting with $0.
0, 10, 2, 12, 4, 14, 6, 16, 8, 18, 10, 20
Explain why this sequence is or is not a function?
A.
This sequence is not a function because the amount $10 appears in the sequence more than once.
B.
This sequence is not a function because the sequence does not form a line.
C.
This sequence is a function because each input (odd terms in sequence) maps to one output (even terms in sequence).
D.
This sequence is a function because each output (even terms in sequence) maps to one input (odd terms in sequence).
the whole question is poorly stated.
each term in the sequence is an output: the savings balance.
so is it D
is it D
1. What are the next three terms in the sequence?
–1, 9, 19, 29, …
38, 37, 32
40, 51, 62
39, 49, 59
38, 47, 56
The sequence is increasing by 10 in each term.
Therefore, the next three terms are 39, 49, 59.
So, the answer is (C) 39, 49, 59.
2. Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 8 bulbs. In the second year, it produced 16 bulbs, and in the third year it produced 32 bulbs. If this pattern continues, how many bulbs should Geoff expect in the sixth year?
64 bulbs
512 bulbs
128 bulbs
256 bulbs
The pattern of the number of bulbs is that it is doubling each year.
So, in the fourth year, the number of bulbs will be 64 (32 x 2).
In the fifth year, the number of bulbs will be 128 (64 x 2).
And, in the sixth year, the number of bulbs will be 256 (128 x 2).
Therefore, Geoff should expect 256 bulbs in the sixth year.
So, the answer is (D) 256 bulbs.
3. What are the first four terms of the sequence represented by the expression n(n – 2) – 3?
–5, –2, 1, 4
–4, –3, 0, 5
–3, 0, 3, 6
–2, 0, 2, 4
If we substitute n = 1, 2, 3, and 4 in the expression, we get:
n(n – 2) – 3 = (1)(–1) – 3 = –4
n(n – 2) – 3 = (2)(0) – 3 = –3
n(n – 2) – 3 = (3)(1) – 3 = 0
n(n – 2) – 3 = (4)(2) – 3 = 5
Therefore, the first four terms of the sequence are –4, –3, 0, 5.
So, the answer is (B) –4, –3, 0, 5.
4. A car traveling at 23 mi/h accelerates to 46 mi/h in 5 seconds. It maintains that speed for 5 seconds and then slows to a stop in 5 seconds. Which graph shows the car’s speed over time?
(Image: A number of points are shown on a graph. The points are connected by line segments.)
(Image: A number of points are shown on a graph. The points are connected by line segments.)
(Image: A number of points are shown on a graph. The points are connected by line segments.)
(Image: A number of points are shown on a graph. The points are connected by line segments.)
The car starts at 23 mi/h and accelerates to 46 mi/h in 5 seconds. This means that its speed increases at a constant rate for 5 seconds. Therefore, the graph should show a straight line with a positive slope for the first 5 seconds.
The car maintains a speed of 46 mi/h for the next 5 seconds. Therefore, the graph should show a horizontal line at y = 46 for the next 5 seconds.
Finally, the car slows down from 46 mi/h to 0 mi/h in 5 seconds. This means that its speed decreases at a constant rate for 5 seconds. Therefore, the graph should show a straight line with a negative slope for the next 5 seconds.
Only option (C) shows the correct pattern for the car's speed over time.
Therefore, the answer is (C).
5. Use the graph below to answer the question that follows.
(Image: A graph titled 'Remote-Control Car' shows 'Time' in seconds from 0 to 10 on the x-axis and 'Speed' in miles per hour from 0 to 10 on the y-axis.)Which statement describes the speed of the remote-control car over time? (1 point)
The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
The speed of the car increases from 4 mi/h to 2 mi/h in the first 3 seconds, decreases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 6 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds.
The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 5 seconds, and then remains at 5 mi/h for the last 10 seconds.
From the graph, we can see that the speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds. This means that the car is slowing down during this time period.
Then, the speed of the car increases to 5 mi/h in the next 2 seconds. This means that the car is accelerating during this time period.
Finally, the speed of the car remains constant at 5 mi/h for the last 5 seconds. This means that the car maintains a constant speed during this time period.
Therefore, the statement that describes the speed of the remote-control car over time is: "The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds."
So, the answer is (A).
6. Given the function rule f(x) = x² – 4x + 3, what is the output of f(–3)?
24
21
0
–3
To find the output of f(–3), we need to substitute x = –3 in the function rule and simplify:
f(–3) = (–3)² – 4(–3) + 3
= 9 + 12 + 3
= 24
Therefore, the output of f(–3) is 24.
So, the answer is (A) 24.
7. Suppose you earn $12 each time you mow the lawn. Which function describes the relationship between your total earnings E and the number of times you mow the lawn, m?
E(m) = m + 12
m = 12E
E(m) = m – 12
E(m) = 12m
If you earn $12 each time you mow the lawn, then your total earnings E will be the product of the number of times you mow the lawn (m) and the amount you earn each time ($12). Therefore, the function that describes the relationship between your total earnings E and the number of times you mow the lawn, m, is:
E(m) = 12m
Therefore, the answer is (D) E(m) = 12m.
8.
The data in the table illustrate a linear function.
x –3 0 3 6
y –6 –2 2 6
What is the slope of the linear function? Which graph represents the data?
(1 point)
(Image: Negative Start Fraction 4 over 3 End Fraction semicolon. A line passes through a graph.)
(Image: Negative Start Fraction 3 over 4 End Fraction semicolon. A line passes through a graph.)
(Image: Start Fraction 3 over 4 End Fraction semicolon. A line passes through a graph.)
(Image: Start Fraction 4 over 3 End Fraction semicolon. A line passes through a graph.)
To find the slope of the linear function, we need to use the slope formula:
slope = (y2 - y1) / (x2 - x1)
We can choose any two points from the table to find the slope. Let's choose (0, -2) and (3, 2):
slope = (2 - (-2)) / (3 - 0)
= 4 / 3
Therefore, the slope of the linear function is 4/3.
The equation of the linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept. We can find the y-intercept by substituting any (x, y) point from the table and solving for b. Let's use (0, -2):
-2 = (4/3)(0) + b
b = -2
Therefore, the equation of the linear function is:
y = (4/3)x - 2
The graph that represents the data is option (A) which has a slope of 4/3 and passes through all the given points:
(Image: Negative Start Fraction 4 over 3 End Fraction semicolon. A line passes through a graph.)
So, the answer is:
The slope of the linear function is 4/3.
The graph that represents the data is (A).
9.
Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft)
Vertical Rise of Street (ft)
Dixie Hill
60
20
Bell Hill
60
40
Liberty Hill
60
30
(1 point)
Bell Hill; it rises (Image: two-thirds) foot for every 1 foot of horizontal travel.
Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
To determine which hill is the steepest, we need to compare the rise over run ratios for each hill, which is a measure of the slope of each hill. The rise over run ratio is the vertical rise of the hill over a given horizontal distance. The larger the ratio, the steeper the hill.
Dixie Hill has a rise of 20 ft over a horizontal distance of 60 ft, which gives a rise over run ratio of 20/60 or 1/3.
Bell Hill has a rise of 40 ft over a horizontal distance of 60 ft, which gives a rise over run ratio of 40/60 or 2/3.
Liberty Hill has a rise of 30 ft over a horizontal distance of 60 ft, which gives a rise over run ratio of 30/60 or 1/2.
Therefore, we can see that Bell Hill has the steepest slope because it has the largest rise over run ratio of 2/3, meaning that it rises 2 feet for every 3 feet of horizontal travel.
So, the answer is:
Bell Hill is the steepest hill because it has the largest rise over run ratio.
10. Which graph represents the linear function y = (Image: one-third)x – 4? (1 point)
(Image: A line on a graph passes through the points left-parenthesis negative 4 comma zero right-parenthesis and left-parenthesis 4 comma 3 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis zero comma negative 4 right-parenthesis and left-parenthesis 3 comma 5 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis negative 3 comma negative 5 right-parenthesis and left-parenthesis zero comma negative 4 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis negative 4 comma zero right-parenthesis and left-parenthesis negative 3 comma 3 right-parenthesis.)
The linear function y = (1/3)x - 4 has a slope of 1/3 and a y-intercept of -4. Therefore, it passes through the point (0, -4) and has a rise of 1 for every horizontal run of 3.
We can eliminate options (B) and (C) because the point (0, -4) is not on the line shown in those graphs.
Option (D) has a slope of 3/1 or 3 and a y-intercept of 0. Therefore, it is not the graph of the given linear function.
Therefore, the correct graph is option (A), which shows a line with a slope of 1/3 passing through the point (-4, 0) and the point (4, 3):
(Image: A line on a graph passes through the points left-parenthesis negative 4 comma zero right-parenthesis and left-parenthesis 4 comma 3 right-parenthesis.)
So, the answer is (A).
11. Which graph represents the linear function y = –5x + 2? (1 point)
(Image: A line on a graph passes through the points left-parenthesis zero comma 2 right-parenthesis and left-parenthesis 1 comma negative 3 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis 1 comma negative 3 right-parenthesis left-parenthesis 2 comma negative 1 right-parenthesis left-parenthesis 3 comma 1 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis negative 5 comma 3 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 5 comma 1 right-parenthesis.)
(Image: A line on a graph passes through the points left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis zero comma negative 2 right-parenthesis.)
The linear function y = -5x + 2 has a slope of -5 and a y-intercept of 2. Therefore, it passes through the point (0, 2) and has a fall of 5 for every horizontal run of 1.
Option (B) and option (D) do not pass through the point (0, 2), so they cannot be the graph of the given linear function.
Option (C) has a rise of 1 for every horizontal run of 5, which is not the slope of the given linear function.
Therefore, the correct graph is option (A), which shows a line with a slope of -5 passing through the point (0, 2) and the point (1, -3):
(Image: A line on a graph passes through the points left-parenthesis zero comma 2 right-parenthesis and left-parenthesis 1 comma negative 3 right-parenthesis.)
So, the answer is (A).
12.
Which function rule represents the data in the table below?
Input (x)
1
2
3
4
5
Output (y)
9
15
21
27
33
y = 4 + 5x
y = 3 + 6x
y = 5 + 4x
y = 6 + 3x
We can see from the table that the output (y) has a constant difference of 6 between each consecutive term. This means that the function is linear and has a constant slope of 6. We can also see from the table that when x = 1, y = 9. This gives us the y-intercept of the function, which is 9.
Therefore, the function rule that represents the data in the table is:
y = 6x + 3
Therefore, the answer is (D) y = 6 + 3x.
13. Max charges $3.50 per hour when he mows lawns, plus $6.00 for transportation expenses. Which function rule represents the amount y Max charges to mow lawns for x hours?
y = 9.50x
y = 6.00x + 3.50
y = 3.50x + 6.00
y = 2.5x
Max charges $3.50 per hour when he mows lawns, plus $6.00 for transportation expenses. Therefore, the total amount y Max charges to mow lawns for x hours is the sum of the cost of mowing the lawn and the transportation expenses, which gives:
y = 3.50x + 6.00
Therefore, the answer is (C) y = 3.50x + 6.00.
14. The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. Which function rule shows how the cost of apples, y, depends on the number of pounds, x?
y = 1.10(x – 1) + 1.35
y = 1.10x + 1.35
y = 1.35x + 1.10
y = (1.10 + 1.35)x