Question

Find the domain and range of 3x - 2y = 17 for (x= -2, -1, 0, 1, 2)

find the domain and range of -2x + 20y = 25 for (x= -2, -1, 0, 1, 2)

Answer 1

AI-generated answer

To find the domain and range of the equation 3x - 2y = 17 for the given values of x (-2, -1, 0, 1, 2), we need to substitute each value of x into the equation and solve for y. Let's go step by step:

1. For x = -2:

3(-2) - 2y = 17

-6 - 2y = 17

-2y = 23

y = -23/2

2. For x = -1:

3(-1) - 2y = 17

-3 - 2y = 17

-2y = 20

y = -10

3. For x = 0:

3(0) - 2y = 17

-2y = 17

y = -17/2

4. For x = 1:

3(1) - 2y = 17

3 - 2y = 17

-2y = 14

y = -7

5. For x = 2:

3(2) - 2y = 17

6 - 2y = 17

-2y = 11

y = -11/2

Now, let's analyze the results:

Domain:

The domain refers to the set of values that x can take. In this case, since we were given specific values for x (-2, -1, 0, 1, 2), the domain is { -2, -1, 0, 1, 2 }.

Range:

The range refers to the set of values that y can take. From our calculations, we found the corresponding values of y for each given x. The range is { -23/2, -10, -17/2, -7, -11/2 }.

Therefore, the domain of the equation 3x - 2y = 17 for the given values of x is { -2, -1, 0, 1, 2 }, and the range is { -23/2, -10, -17/2, -7, -11/2 }.

Explanation:

To find the domain and range of the equation -2x + 20y = 25 for the given values of x (-2, -1, 0, 1, 2), we need to substitute each value of x into the equation and solve for y. Let's go step by step:

1. For x = -2:

-2(-2) + 20y = 25

4 + 20y = 25

20y = 21

y = 21/20

2. For x = -1:

-2(-1) + 20y = 25

2 + 20y = 25

20y = 23

y = 23/20

3. For x = 0:

-2(0) + 20y = 25

0 + 20y = 25

20y = 25

y = 25/20 = 5/4

4. For x = 1:

-2(1) + 20y = 25

-2 + 20y = 25

20y = 27

y = 27/20

5. For x = 2:

-2(2) + 20y = 25

-4 + 20y = 25

20y = 29

y = 29/20

Now, let's analyze the results:

Domain:

The domain refers to the set of values that x can take. In this case, since we were given specific values for x (-2, -1, 0, 1, 2), the domain is { -2, -1, 0, 1, 2 }.

Range:

The range refers to the set of values that y can take. From our calculations, we found the corresponding values of y for each given x. The range is { 21/20, 23/20, 5/4, 27/20, 29/20 }.

Therefore, the domain of the equation -2x + 20y = 25 for the given values of x is { -2, -1, 0, 1, 2 }, and the range is { 21/20, 23/20, 5/4, 27/20, 29/20 }.

Answer 2

1. Domain: {-2, -1, 0, 1, 2} Range: {-23/2, -10, -17/2, -7, -11/2}

2. Domain: {-2, -1, 0, 1, 2} Range: {21/20, 23/20, 5/4, 27/20, 29/20}

Explanation:

For the equation 3x - 2y = 17:

Given equation: 3x - 2y = 17

We can rearrange this equation to solve for y:

3x - 17 = 2y

y = (3x - 17)/2

Now, we can calculate the values of y for each x:

For x = -2:

y = (3(-2) - 17)/2 = (-6 - 17)/2 = -23/2

For x = -1:

y = (3(-1) - 17)/2 = (-3 - 17)/2 = -20/2 = -10

For x = 0:

y = (3(0) - 17)/2 = (-17)/2 = -17/2

For x = 1:

y = (3(1) - 17)/2 = (3 - 17)/2 = -14/2 = -7

For x = 2:

y = (3(2) - 17)/2 = (6 - 17)/2 = -11/2

Now, let's determine the domain and range:

Domain: These are the possible values of x. In this case, the given values of x are -2, -1, 0, 1, and 2.

Domain: {-2, -1, 0, 1, 2}

Range: These are the corresponding values of y that we calculated for each x.

Range: {-23/2, -10, -17/2, -7, -11/2}

For the equation -2x + 20y = 25:

Given equation: -2x + 20y = 25

We can rearrange this equation to solve for y:

20y = 2x + 25

y = (2x + 25)/20

Now, we can calculate the values of y for each x:

For x = -2:

y = (2(-2) + 25)/20 = (-4 + 25)/20 = 21/20

For x = -1:

y = (2(-1) + 25)/20 = (-2 + 25)/20 = 23/20

For x = 0:

y = (2(0) + 25)/20 = (25)/20 = 5/4

For x = 1:

y = (2(1) + 25)/20 = (2 + 25)/20 = 27/20

For x = 2:

y = (2(2) + 25)/20 = (4 + 25)/20 = 29/20

Now, let's determine the domain and range:

Domain: These are the possible values of x, which are -2, -1, 0, 1, and 2.

Domain: {-2, -1, 0, 1, 2}

Range: These are the corresponding values of y that we calculated for each x.

Range: {21/20, 23/20, 5/4, 27/20, 29/20}