Evaluate the piecewise defined function at the indicated values
F(x)=6x If x<-4
X+3 If -4<equal to x< equal to 4
(X-4)^2 If x>4
f(-5)
f(-4)
f(3)
f(4)
f(7)
To evaluate the function at the indicated values, we will use the given piecewise definitions:
1. For x < -4, F(x) = 6x
a) f(-5): Since -5 is less than -4, we use the first definition.
F(-5) = 6(-5) = -30
Therefore, f(-5) = -30
2. For -4 ≤ x ≤ 4, F(x) = x + 3
b) f(-4): Since -4 is inclusive in this interval, we use the second definition.
F(-4) = -4 + 3 = -1
Therefore, f(-4) = -1
c) f(3): Since 3 falls within this interval, we also use the second definition.
F(3) = 3 + 3 = 6
Therefore, f(3) = 6
3. For x > 4, F(x) = (x - 4)^2
d) f(4): Since 4 is not greater than 4, we cannot use the third definition. However, since 4 is inclusive in the previous interval, we use the second definition again.
F(4) = 4 + 3 = 7
Therefore, f(4) = 7
e) f(7): Since 7 is greater than 4, we use the third definition.
F(7) = (7 - 4)^2 = 3^2 = 9
Therefore, f(7) = 9
In summary:
f(-5) = -30
f(-4) = -1
f(3) = 6
f(4) = 7
f(7) = 9
To evaluate the piecewise defined function at the indicated values, we substitute the given values into the corresponding parts of the function.
For f(-5), since -5 is less than -4, we use the first part of the function:
f(-5) = 6(-5) = -30.
For f(-4), since -4 is equal to -4, we use the second part of the function:
f(-4) = -4 + 3 = -1.
For f(3), since 3 is greater than -4 and less than or equal to 4, we use the second part of the function:
f(3) = 3 + 3 = 6.
For f(4), since 4 is equal to 4, we use the second part of the function:
f(4) = 4 + 3 = 7.
For f(7), since 7 is greater than 4, we use the third part of the function:
f(7) = (7 - 4)^2 = 9.
Therefore, the evaluations of the function at the given values are:
f(-5) = -30
f(-4) = -1
f(3) = 6
f(4) = 7
f(7) = 9.