I. Evaluate the following piece-wise function. (5 points) x+5x-8 when, x+5 when, x>3 20 when, x=3 8x+7 when, -2≤ x< 2 x²+3x-9 when, x<-2 x=2 Find; 1. f(-4) 2. f(1) 3.f(3) 4. f(6)
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I. Evaluate the following piece-wise function. (5 points) x+5x-8 when, x+5 when, x>3 20 when, x=3 8x+7 when, -2≤ x< 2 x²+3x-9 when, x<-2 x=2 Find; 1. f(-4) 2. f(1) 3.f(3) 4. f(6)
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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: