Verified answer

Answer:

To evaluate the piece-wise function for different values of x, we need to follow the defined conditions:

1. For x < -2:

  f(x) = x² + 3x - 9

2. For -2 ≤ x < 2:

  f(x) = 8x + 7

3. For x = 2:

  f(x) = 20

4. For x > 3:

  f(x) = x + 5

Now, let's find the values for the given x:

1. f(-4) [x < -2]:

  f(-4) = (-4)² + 3(-4) - 9

  f(-4) = 16 - 12 - 9

  f(-4) = -5

2. f(1) [-2 ≤ x < 2]:

  f(1) = 8(1) + 7

  f(1) = 8 + 7

  f(1) = 15

3. f(3) [x = 3]:

  f(3) = 20

4. f(6) [x > 3]:

  f(6) = 6 + 5

  f(6) = 11

So, the values of the piece-wise function for the given x are:

1. f(-4) = -5

2. f(1) = 15

3. f(3) = 20

4. f(6) = 11

Answer:To evaluate the piece-wise function for different values of x, we need to follow the defined conditions:

1. For x < -2:

  f(x) = x² + 3x - 9

2. For -2 ≤ x < 2:

  f(x) = 8x + 7

3. For x = 2:

  f(x) = 20

4. For x > 3:

  f(x) = x + 5

Now, let's find the values for the given x:

1. f(-4) [x < -2]:

  f(-4) = (-4)² + 3(-4) - 9

  f(-4) = 16 - 12 - 9

  f(-4) = -5

2. f(1) [-2 ≤ x < 2]:

  f(1) = 8(1) + 7

  f(1) = 8 + 7

  f(1) = 15

3. f(3) [x = 3]:

  f(3) = 20

4. f(6) [x > 3]:

  f(6) = 6 + 5

  f(6) = 11

So, the values of the piece-wise function for the given x are:

1. f(-4) = -5

2. f(1) = 15

3. f(3) = 20

4. f(6) = 11

Step-by-step explanation: