For the piecewise function, find the values g(-8), 8(3), and g(8).
g(x)={X+6,FOR X<=3
7-x, for x>3
for x = -8 and x = 3
x ≤ 3
so use
g(x) = x + 6
g(-8) = -8 + 6
and g(3) = 3 + 6
for x = 8
x > 3
so use
g(x) = 7-x
g(8) = 7-8
To find the values g(-8), g(3), and g(8) for the given piecewise function, follow these steps:
1. First, determine which condition of the function applies to the given value.
- For g(-8):
Since -8 is less than or equal to 3, the condition g(x) = x + 6 applies.
- For g(3):
Since 3 is equal to 3, the condition g(x) = x + 6 applies.
- For g(8):
Since 8 is greater than 3, the condition g(x) = 7 - x applies.
2. Substitute the value into the corresponding equation:
- For g(-8):
Substituting -8 into the equation g(x) = x + 6:
g(-8) = -8 + 6 = -2
- For g(3):
Substituting 3 into the equation g(x) = x + 6:
g(3) = 3 + 6 = 9
- For g(8):
Substituting 8 into the equation g(x) = 7 - x:
g(8) = 7 - 8 = -1
Therefore, g(-8) = -2, g(3) = 9, and g(8) = -1.
To find the values g(-8), g(3), and g(8), we need to substitute these values into the given piecewise function:
1. Let's start with g(-8). Since -8 is less than or equal to 3, we will use the first part of the function g(x)=x+6.
Substitute -8 into the function: g(-8) = -8 + 6 = -2.
Therefore, g(-8) = -2.
2. Next, let's find g(3). Since 3 is equal to 3, we will use the first part of the function g(x)=x+6.
Substitute 3 into the function: g(3) = 3 + 6 = 9.
Therefore, g(3) = 9.
3. Lastly, we need to find g(8). Since 8 is greater than 3, we will use the second part of the function g(x)=7-x.
Substitute 8 into the function: g(8) = 7 - 8 = -1.
Therefore, g(8) = -1.
In summary:
g(-8) = -2
g(3) = 9
g(8) = -1