[ad_1]

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

[ad_2]

# Tag: xaxis

[ad_1]

**Answer:**

**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.**

[ad_2]

[ad_1]

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.

[ad_2]

[ad_1]

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

[ad_2]

[ad_1]

**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. **

[ad_2]

[ad_1]

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.

[ad_2]

[ad_1]

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.

[ad_2]

[ad_1]

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

[ad_2]

[ad_1]

**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. **

[ad_2]

[ad_1]

(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

[ad_2]

[ad_1]

**Answer:**

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.**

[ad_2]

[ad_1]

**Answer:**

**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.**

[ad_2]