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Coordinate Algebra EOC (GSE) Quiz Answer KeyFunctions - (MGSE9‐12.F.IF.9) Compare Properties

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

x y

2 2

3 4

4 6

5 8

Which function corresponds with the table?

A) f(x) = x + 2

B) f(x) = 2x - 2

C) f(x) = -2x + 2

D) f(x) = -2x - 1

Explanation:The function that corresponds with the table is f(x) = 2x - 2. We can use the slope formula to find the slope (2). After finding theslope we can use any point to form an equation of the line using slope-intercept form.



2)

Company 2

# of textmessages

Price($)

0 - 100 5

101 - 200 10

201 - 300 15

301 - 400 20

401 - 500 25

Two companies offer different charges for text messaging. Company 1 charges $0.04 per text message, while Company 2 chargesrates according to the table.

Which company offers the cheapest plan for up to 500 text messages?

A) Company 1 because the cost of 500 text messages is $15.

B) Company 1 because the cost of 500 text messages is $20.

C) Company 2 because the cost of 500 text messages is $25.

D) The costs for both plans are exactly the same for 500 text messages.

Explanation:Company 1 because the cost of 500 text messages is $20. Company 2 charges $25.

3)

Consider the two functions shown here. Which function has the greater rate of change? Explain your answer.

A) Function 1, because the rate of change is 2.

B) Function 2, because the rate of change is ½.

C) Function 2, because the rate of change is 7.

D) Function 1, because the rate of change is ½ .

Explanation:Function 1 because the rate of change is 2. If you determine the ratio of the rise to the run of function 1 the slope is 2. Function 2



has a slope of ½, which is less than 2.



4) Function 1: y = 4x + 5Function 2: The line passing through the points (1, 6) and (3, 10).

Which of these functions has the greater rate of change?

A) Function 1, because the slope is 5 and the slope of function 2 is 4.

B) Function 1, because the slope is 4 and the slope of function 2 is 2.

C) Function 2, because the slope is 7 and the slope of function 1 is 5.

D) Function 2, because the slope is 5 and the slope of function 1 is 4.

Explanation:Function 1, because the slope is 4 and the slope of function 2 is 2. Use the slope formula.

5)

x y

0 3

1 1

2 -1

Which function corresponds to the table?

A) y = 3x - 2

B) y = 2x + 3

C) y = -2x + 3

D) y = -3x + 2

Explanation:The line that corresponds with the table is y= -2x + 3. We can use the slope formula to find the slope (-2). After finding the slope wecan use the the point (0,3) to form an equation of the line using slope-intercept form.

6)

Scenario 1

Scenario 2y = 50x

x is time in hoursy is distance in miles



Compare the scenarios and determine which shows the greater speed.

A) Scenario 1 because the slope is 60.

B) Scenario 2 because the slope is 50.

C) Scenario 1 because the slope is 1

60.

D) Scenario 2 because the slope is 1

50.

Explanation:Scenario 1 because the slope is 60. The slope for scenario 1 is 60, whereas the slope of the function in scenario 2 is 50 miles perhour.



7)

Company 2

# of textmessages

Price($)

0 - 100 5

101 - 200 10

201 - 300 15

301 - 400 20

401 - 500 25

Two companies offer different charges for text messaging. Company 1 charges $0.06 per text message, while Company 2 chargesrates according to the table.

Which company offers the cheapest plan for 500 text messages?

A) Company 2, because the other company would charge $30.

B) Company 1, because the cost of 500 text messages is $25.

C) Company 2, because the cost of 500 text messages is $20.

D) Company 1, because the cost of each text message is only $0.06.

Explanation:Company 2, because the other company would charge $30. Multiply to compare.



8)

function f

x y

1 4

3 10

5 16

7 22

9 28

The table shows values for the function f, while the graph shows function g.

Which function has the greater slope?

A) f

B) g

C) They are the same.

D) Insufficient information.

Explanation:f has the greater slope, 3. The slope of g is 2.



9)

Car B

Distance (miles) Time (hours)

7.5 1

15 2

22.5 3

30 4

Compare the graph of Car A to the table of Car B to determine which car is traveling at the greatest speed and by how much.

A) Car A is going 2 times faster than Car B

B) Car A is going 3 times faster than Car B

C) Car B is going 2 times faster than Car A

D) Car B is going 3 times faster than Car A

Explanation:Car A is going 2 times faster than Car B is correct. Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (105-15)/(7-1) = 90/6= 15 mph; Car B's speed is, s = d/t = 22.5/3 = 7.5 mph. Thus, Car B is traveling 3 times faster than Car A.



10)

Car Speed

Distance (m) Time (s)

Car B 45 meters 3 seconds

Car C 80 meters 4 seconds

Car D 30 meters 6 seconds

Compare the graph of Car A to the table of Car B, C & D to determine which car is traveling at the greatest speed.

A) Car A

B) Car B

C) Car C

D) Car D

Explanation:Car C is correct. Car C is traveling at s = d/t = 80/4 = 20 m/s; Car B is traveling at s = d/t = 45/3 = 15 m/s; Car D is traveling at s = d/t= 30/6 = 5 m/s; and Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (70-40)/(7-4) = 30/3 = 10 m/s



11)

Car Speed

Distance (m) Time (s)

Car B 30 meters 3 seconds

Car C 60 meters 4 seconds

Car D 90 meters 6 seconds


A) Car A

B) Car B

C) Car C

D) Car D

Explanation:Car A is correct. Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (150-50)/(6-2) = 100/4 = 25 m/s; Car B is traveling at s =d/t = 30/3 = 10 m/s; Car C is traveling at s = d/t = 60/4 = 15 m/s; Car D is traveling at s = d/t = 90/6 = 15 m/s.



12)

Function 2

x y

0 0

1 1

2 4

3 9

4 16

6 36

8 64

Consider the two functions shown here. Which function grows faster for large positive values of x? [Note: Function 1 is shown in thegraph.]

A) Function 1, because it has larger x values than function 2.

B) Function 1, because the y-value for x = 1 is greater in function 1.

C) Function 2, because all the range values of the function are positive.

D) Function 2, because the y-values increase faster than the y-values in function 1.

Explanation:Function 2, because the y-values increase faster than the y-values in function 1. The values in the table are being squared, while theones in the graph are from the linear function y = 4x + 5.



13)

Car B

Car B

y = 30x; x = time in hours, y = distance in miles






Explanation:Car B is going 2 times faster than Car A is correct. Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (105-15)/(7-1) = 90/6= 15 mph; Car speed in the table is in Slope-Intercept Form y = mx + b where m is the slope or speed. Thus, Car B is traveling at 30mph, 2 times faster than Car A.



14)

Car B

Distance (miles) Time (hours)

45 1

90 2

135 3

180 4






Explanation:Car B is going 3 times faster than Car A is correct. Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (105-15)/(7-1) = 90/6= 15 mph; Car B's speed is, s = d/t = 180/4 = 45 mph. Thus, Car B is traveling 3 times faster than Car A.

15) Which function has the largest slope?

A) y = 4x + 5

B) y = 3x + 25

C) y = 8x + 2

4

D) A function showing a rock collection growing by five rocks each day.

Explanation:A function showing a rock collection growing by five rocks each day.



16)

Car Speed

Car B Car C Car D

y = 12.5x; x = time in hours, y =distance in miles

y = 20x; x = time in hours, y =distance in miles

y = 30x; x = time in hours, y =distance in miles


A) Car A

B) Car B

C) Car C

D) Car D

Explanation:Car D is correct. Car A's speed is the slope of the graph, s = (y2-y1)/(x2-x1) = (150-50)/(6-2) = 100/4 = 25 mph; Car speed in the tableis in Slope-Intercept Form y = mx + b where m is the slope or speed. Car B is traveling at 12.5 mph; Car C is traveling at 20 mph; CarD is traveling at 30 mph.

17) Are Functions 1 and 2 the same? Explain.

Function 1: y = 3(x + 5)Function 2: y equals three times x, plus 5.

A) No, 3(x + 5) = 15x and “three times x, plus 5” would be 3x + 5.

B) Yes, 3(x + 5) and “three times x, plus 5” are both equal to 15x.

C) Yes, 3(x + 5) and “three times x, plus 5” are both equal to 3x + 5.

D) No, 3(x + 5) = 3x + 15 and “three times x, plus 5” would be 3x + 5.

Explanation:No, 3(x + 5) = 3x + 15 and “three times x, plus 5” would be 3x + 5.

18)



Jenny solved a system consisting of the equation y = log2(x) and the graph shown. She insists that the complete solution consists

only of the point (4, 2).

Is she correct? Why or why not?

A) No, she is not correct as the two functions only intersect at that one point.

B) Yes, she is correct since that is the only point that the two functions intersect at.

C)No, she is not correct. The logarithmic function is the slowest growing function therefore the two graphs must intersect atanother point as the function graphed must over take the log as x → ∞.

D)Yes, she is correct. The function shown in the graph grows at a slower rate than the logarithmic function . Therefore as x→ ∞ all the y-values in the function graphed must be lower than the log y-values which is the case.

Explanation:The two functions being compared are the square root function and the logarithmic function. The logarithmic function is the slowestgrowing function so a s → ∞ it should have smaller y-values than the square root function.

Therefore, No, she is not correct. The logarithmic function is the slowest growing function therefore the two graphs must intersect atanother point as the function graphed must over take the log as x → ∞.



19)

x f(x)

2 7

3 12

4 19

5 28

Compare the function represented by the table to the function represented by the graph to determine which statement is true.

A) The tabled function has a lessor minimum value.

B) The tabled function has a greater maximum value.

C) The graphed function has a lessor minimum value.

D) The graphed function has a greater maximum value.

Explanation:The tabled function has a greater maximum value.

First, write a function to represent the table.

Then, use -b

2a to find the vertex from the equation of a parabola.

tabled function: f(x) = x2 + 3: Range y ≤ 3

graphed function: Range y ≤ 1

20)

x f(x)

2 6

3 11



4 18

5 27






Explanation:The graphed function has a lessor minimum value.


Then, use -b


tabled function: f(x) = x2 + 2: Range y ≥ 2

graphed function: Range y ≥ -.25.



21)

Compare the algebraically expressed function f(x) = 3x2 + 6x + 7 to the function shown in the graph to determine which statement istrue.

A) The algebraic function has a greater maximum value.

B) The algebraic function has a lessor minimum value.

C) The graphed function has a greater maximum value.

D) The graphed function has a lessor minimum value.


Use -b


f(x) = 3x2 + 6x + 7: Range y ≥ 4

graphed function: Range y ≥ -2

22)

Compare the algebraically expressed function f(x) = -8x2 + 4x + 2 to the function shown in the graph to determine which statementis true.





Explanation:The algebraic function has a greater maximum value.

Use -b




f(x) = -8x2 + 4x + 2: Range y ≤ 5

2

graphed function: Range y ≤ -3

8



23)

Function A is a quadratic function that passes through the points (-1, 11) (2, 5) and (3, 11). Function B is an absolute value functionwith a vertex at (1, 3), a vertical stretch of 2, and a y-intercept at (0, 5).

For which interval is A > B?

A) (0, 2)

B) (2, ∞)

C) (-∞, 0]

D) (0,1) ∪ (1,2)

Explanation:(2, ∞)

Function A has the equation y = 2x2 -4x +5 and Function B has the equation y = 2|x - 1| + 3.

The two functions are shown in the graph.



For A > B, the y-values of A need to be LARGER than the y-values of B. This occurs from (-∞, 0) and (2, ∞). Neither 0 nor 2 can be

included.

24)

x f(x)

2 3

3 8

4 15

5 24










Then, use -b


tabled function: f(x) = x2 - 1: Range y ≥ -1

4




25)

Compare the algebraically expressed function f(x) = 1

4x2 - 2x to the function shown in the graph to determine which statement is

true.






Use -b


f(x) = 1

4x2 - 2x: Range y ≥ -4


26)

x f(x)

2 -3

3 -8

4 -15

5 -24








Explanation:The tabled function has a greater maximum value.


Then, use -b


tabled function: y = -x2 + 1: Range y ≤ 1

graphed function: Range y ≤ 1

2



27)

Compare the algebraically expressed function f(x) = -5

2x2 - 8x to the function shown in the graph to determine which statement is

true.





Explanation:The algebraic function has a greater maximum value.

Use -b


f(x) = -5

2x2 - 8x: Range y ≤

32

5

graphed function: Range y ≤ 5.

28)

x y

1 1

2 4

3 9

4 16

An exponential function has the equation y = (0.5)x - 1. Another function is shown in the table.

For what values of x will the two functions be equal?

A) x = 0

B) x = -1, 0

C) x = 0, 1

D) The functions are never equal.

Explanation:

The function shown in the table is a quadratic y = x2.

A graph of the two functions is shown below. The solutions are the intersection points.



x = -1, 0



29) Function A is a quadratic function with a vertex at (3, 4) and a leading coefficient of -1

Function B has the equation y = |x + 2|.

Function A is then reflected over the x-axis and shifted down 2 while function B is reflected over the x-axis and shifted up 3.

Which function has the larger y-intercept after being transformed and by how much?

A) A, 2 units

B) A, 3 units

C) B, 2 units

D) B, 1 unit

Explanation:A, 2 units

Function A has the equation y = -(x - 3)2 + 4. After transformation the equation becomes y = (x - 3)2 - 6

Function B after transforming has the equation y = -|x + 2| + 3.

If you plug in 0 for x in both equations you get A has a y-intercept of 3 and B has a y-intercept of 1.

30)

Function A is a quadratic function that passes through the points (-1, 11) (2, 5) and (3, 11). Function B is an absolute value functionwith a vertex at (1, 3), a vertical stretch of 2, and a y-intercept at (0, 5).

For which interval is A < B?

A) (0, 2)

B) (2, ∞)

C) (-∞, 0]

D) (0,1) ∪ (1,2)

Explanation:(0,1) ∪ (1,2)

Function A has the equation y = 2x2 -4x +5 and Function B has the equation y = 2|x - 1| + 3.



The two functions are shown in the graph.

For A < B, the y-values of A need to be SMALLER than the y-values of B. This occurs from (0, 1) ∪ (1,2). 1 must be excluded since the

y-values are equal at that point.

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