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## The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 6x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? A. 5 B. 6 C. 7 D. 8

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 6x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? A. 5 B. 6 C. 7 D. 8

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## The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range but not the domain of the transformed function is the same as that of the parent function. The domain but not the range of the transformed function is the same as that of the parent function.

D. The domain but not the range of the transformed function is the same as that of the parent function.

Step-by-step explanation:

We are given,

The function is reflected across x-axis, which gives .

And then the function is translated to the right by 6 units, which gives .

Thus, the transformed function is

So, from the graph shown below, we get,

Domain of both the functions f(x) and g(x) is set of all real numbers.

Range of f(x) is .

But, Range of g(x) is .

Hence, the correct option is,

D. The domain but not the range of the transformed function is the same as that of the parent function.

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## Which of the following statements best describes the graph of x + y = 2? A. It is a line which intersects the x-axis at (2, 2). B. It is a line which intersects the y-axis at (2, 2). C. It is a line joining the points whose x- and y-coordinates add up to 2. D. It is a line joining the points whose x- and y-coordinates add up to 4.

Which of the following statements best describes the graph of x + y = 2? A. It is a line which intersects the x-axis at (2, 2). B. It is a line which intersects the y-axis at (2, 2). C. It is a line joining the points whose x- and y-coordinates add up to 2. D. It is a line joining the points whose x- and y-coordinates add up to 4.

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## Which function represents g(x), a reflection of f(x) = 4 across the x-axis? g(x) = −4(2)x g(x) = 4(2)−x g(x) = −4 g(x) = 4

Which function represents g(x), a reflection of f(x) = 4 across the x-axis? g(x) = −4(2)x g(x) = 4(2)−x g(x) = −4 g(x) = 4

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## A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. How many units to the right of a vertical line through (k, 0) must the fourth vertex be?

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## Which equation does the graph below represent? A coordinate grid is shown. The x-axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y-axis values are from negative 15 to positive 15 in increments of 3 for each grid line. A line is shown passing through the ordered pairs negative 4, 12 and 0, 0 and 4, negative 12. y = fraction negative 1 over 3x y = −3x y = 3x y = fraction 1 over 3x

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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## The graph shows the distance y, in miles, of a moving train from a station over a certain period of time, x, in hours: A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 40, 80, 120, 160, 200, 240, 280, 320. The graph shows a straight line joining the ordered pairs 0, 80, and 1, 120, and 2, 160, and 3, 200, and 4, 240. What is the speed (in miles per hour) of the train and why? 80 miles per hour, because speed is the initial value of the function 120 miles per hour, because speed is the distance traveled in unit time 240 miles per hour, because speed is the distance traveled in a certain time 40 miles per hour, because speed is the rate of change of distance

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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## If the parent function is y=1/x, describe the change in the equation y=-1/x A. Reflects across the y-axis B. Reflects across the x-axis C. Moves 1 unit down D. Moves 1 unit to the left

If the parent function is y=1/x, describe the change in the equation y=-1/x A. Reflects across the y-axis B. Reflects across the x-axis C. Moves 1 unit down D. Moves 1 unit to the left

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## What is the transformation that occurs to the parent function y =(1/2)^x power if the equation changes to y =(1/2)^-x? A. The graph moves 1 unit up. B. The graph reflects across the y-axis. C. The graph reflects across the x-axis. D. The graph moves 1 unit down.

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## (02.02 MC) Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below: Figure 1 is at (5, 8) (4, 4) (6, 2) (7, 6) . Figure 2 is at (-5, -2) (-7, -4) (-4, -6) (-6, -8) . Which two transformations can map figure 1 onto figure 2? (6 points) A) Reflection across the y-axis, followed by translation 10 units down B) Reflection across the y-axis, followed by reflection across x-axis C) Reflection across the x-axis, followed by reflection across y-axis D) Translation 11 units left, followed by translation 10 units down

(02.02 MC) Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below: Figure 1 is at (5, 8) (4, 4) (6, 2) (7, 6) . Figure 2 is at (-5, -2) (-7, -4) (-4, -6) (-6, -8) . Which two transformations can map figure 1 onto figure 2? (6 points) A) Reflection across the y-axis, followed by translation 10 units down B) Reflection across the y-axis, followed by reflection across x-axis C) Reflection across the x-axis, followed by reflection across y-axis D) Translation 11 units left, followed by translation 10 units down

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## Please help! URGENT! Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply. A. The function in vertex form is f(x) = (x – 4)2 – 11. B. The vertex of the function is (–8, 5). C. The axis of symmetry is x = 5. D.The y-intercept of the function is (0, 5). E. The function crosses the x-axis twice.

Options A, D and E

Step-by-step explanation:

The given function is f(x) = x² – 8x + 5

We will convert this equation of a parabola into the vertex form which is

f(x) = (x – h)² + k

f(x) = x² – 8x + 5

= x² – 2(4x) + 16 – 16 + 5

f(x) = (x – 4)² – 11

Therefore, vertex of the parabola will be (4, -11) and axis of symmetry will be x = 4

Now we check the options given

A). True. Vertex form of the equation is f(x) = (x – 4)² – 11

B). False. Vertex of the parabola is (4, -11)

C). False. Axis of symmetry of the parabola is x = 4

D). For y – intercept of any function x coordinates will be 0 (x = 0)

We put x = 0 in the given function.

f(x) = 0 – 0 + 5

f(x) = 5

So y intercept of the function is (0, 5).

Therefore, this option is True.

E. For x- intercepts there should be f(x) = 0

Therefore, (x – 4)²- 11 = 0

(x – 4)² = 11

x – 4 = ±√11

x = 4 ± √11

This proves that function crosses the x axis twice.

So the given option is True.

Options A, D and E are correct.

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## PLEASE HELPPP Which graph has a negative rate of change for the interval 0 to 2 on the x-axis?

D is correct. x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

Step-by-step explanation:

We are given a linear function and an exponential function in graph.

We need to find interval when growth rate of the exponential function exceed the growth rate of the linear function.

Option A) When x<1

Growth rate of linear function = 2

Growth rate of Exponential function = 0.75

When x<1 , growth rate of exponential function is less than linear function.

Option B) When 0≤x≤1

Growth rate of linear function = 2

Growth rate of Exponential function = 1

When 0≤x≤1  , growth rate of exponential function is less than linear function.

Option C) When 1≤x≤2

Growth rate of linear function = 2

Growth rate of Exponential function = 2

When 1≤x≤2  , growth rate of exponential function is equal to linear function.

Option D) When x>2

Growth rate of linear function = 2

Growth rate of Exponential function = 4

When x>2  , growth rate of exponential function is exceed the growth rate of  linear function.

Thus, x>2 the growth rate of the exponential function exceed the growth rate of the linear function.