g(x)= {x+6, x is less or equal to -4
{1-2x -4, x> -4
To evaluate the function g(x), we need to substitute the given x value into the appropriate expression based on the conditions provided.
Let's consider two cases:
1. Case: x is less than or equal to -4
For this case, the expression to use is g(x) = x + 6.
2. Case: x is greater than -4
For this case, the expression to use is g(x) = 1 - 2x - 4.
Now, let's solve some examples to demonstrate how to evaluate the function for specific values of x.
Example 1: Evaluate g(x) for x = -5
Since -5 is less than -4, we will use the first expression: g(x) = x + 6.
Substituting -5 into the expression:
g(-5) = -5 + 6 = 1
Example 2: Evaluate g(x) for x = 0
Since 0 is greater than -4, we will use the second expression: g(x) = 1 - 2x - 4.
Substituting 0 into the expression:
g(0) = 1 - 2(0) - 4 = 1 - 0 - 4 = -3
Example 3: Evaluate g(x) for x = -4
Since -4 is equal to -4, we will use the first expression: g(x) = x + 6.
Substituting -4 into the expression:
g(-4) = -4 + 6 = 2
By following these steps, you can evaluate the function g(x) for any given value of x based on the conditions provided.