Given the piecewise function h(x):
-When x is less than "-3", h(x)=-5x-13
-When x is between -3 and 5, h(x)=5
-When x is greater than or equal to 5, h(x)=x+1
1) For h(-6), this notation indicates that you have to determine the value of h(x) when x=-6
-6 is less than -3, which means that for this value of x, the function has the following shape
Replace the expression with x=-6 and calculate the corresponding value of x:
2) For h(0), you have to determine the value of h(x) when x=0. Zero is between -3 and 5, for this value of x, the function h(x) has the following shape:
This equation represents a horizontal line, which means that for every value within the interval of definition -3≤x<5, the function always has the same value h(x)=5
We can conclude that:
3) For h(5), you have to determine the value of h(x) for x=5, for values of x greater than or equal to 5, h(x) has the following shape:
Replace the expression with x=5 and calculate the corresponding value of h(x):
4) For h(9), you have to determine the value of h(x) when x=9, 9 is greater than 5, for this value of x, the function has the following shape:
Replace the expression with x=9, and calculate the corresponding value of h(x):
So, to sum up: