Evaluate the piecewise defined function at the indicated values.
f(x) = x2 + 6x if x ≤ −1
x if −1 < x ≤ 1
−1 if x > 1
f(−2) =
f(-3/2) =
f(−1) =
f(0) =
f(35) =
what's the problem? Pick a value for x and use the relevant function.
f(-1) = x^2+6x = -5
f(0) = x = 0
Evaluate the piecewise defined function at the indicated values.
f(x) =
x2 if x < 0
x + 6 if x ≥ 0
f(−2) =
f(−1) =
f(0) =
f(1) =
f(2) =
To evaluate the piecewise defined function at the indicated values, we need to substitute the given values into the corresponding parts of the function.
Given:
f(x) = x^2 + 6x if x ≤ -1
x if -1 < x ≤ 1
-1 if x > 1
Evaluation:
1. f(-2):
Since -2 ≤ -1, we use the first part of the function:
f(-2) = (-2)^2 + 6(-2)
= 4 - 12
= -8
2. f(-3/2):
Since -1 < -3/2 ≤ 1, we use the second part of the function:
f(-3/2) = -3/2
3. f(-1):
Since -1 ≤ -1, we use the first part of the function:
f(-1) = (-1)^2 + 6(-1)
= 1 - 6
= -5
4. f(0):
Since -1 < 0 ≤ 1, we use the second part of the function:
f(0) = 0
5. f(35):
Since 35 > 1, we use the third part of the function:
f(35) = -1
Therefore:
f(-2) = -8
f(-3/2) = -3/2
f(-1) = -5
f(0) = 0
f(35) = -1
To evaluate the piecewise defined function at the indicated values, we need to consider the conditions specified for each part of the function.
1. f(-2):
Since -2 is less than or equal to -1, we use the first part of the function: f(x) = x^2 + 6x
Plugging -2 into the function, we get:
f(-2) = (-2)^2 + 6(-2)
= 4 - 12
= -8
Therefore, f(-2) = -8.
2. f(-3/2):
Since -3/2 is greater than -1 but less than or equal to 1, we use the second part of the function: f(x) = x
Plugging -3/2 into the function, we get:
f(-3/2) = -3/2
Therefore, f(-3/2) = -3/2.
3. f(-1):
Since -1 is equal to -1, we use the second part of the function: f(x) = x
Plugging -1 into the function, we get:
f(-1) = -1
Therefore, f(-1) = -1.
4. f(0):
Since 0 is greater than -1 but less than or equal to 1, we use the second part of the function: f(x) = x
Plugging 0 into the function, we get:
f(0) = 0
Therefore, f(0) = 0.
5. f(35):
Since 35 is greater than 1, we use the third part of the function: f(x) = -1
Plugging 35 into the function, we get:
f(35) = -1
Therefore, f(35) = -1.
In summary,
f(-2) = -8,
f(-3/2) = -3/2,
f(-1) = -1,
f(0) = 0,
f(35) = -1.