g(x)= {x+6, x is less or equal to -4
{1/2x -4, x> -4
To evaluate the function g(x) at a specific value, you need to follow the given rules:
1. If x is less than or equal to -4, use the first part of the function: g(x) = x + 6.
2. If x is greater than -4, use the second part of the function: g(x) = (1/2)x - 4.
Let's try a few examples:
Example 1: Find g(3).
Since 3 is greater than -4, we'll use the second part of the function:
g(3) = (1/2)(3) - 4
= 3/2 - 4
= -5/2
Therefore, g(3) = -5/2.
Example 2: Find g(-5).
Since -5 is less than or equal to -4, we'll use the first part of the function:
g(-5) = (-5) + 6
= 1
Therefore, g(-5) = 1.
Example 3: Find g(-4).
Since -4 is equal to -4, we can use either part of the function.
Let's use the first part:
g(-4) = (-4) + 6
= 2
Alternatively, using the second part:
g(-4) = (1/2)(-4) - 4
= -2 - 4
= -6
Therefore, g(-4) can be either 2 or -6.
I hope this helps you understand how to evaluate the given function g(x) for different values of x.