Respuesta :
Given the piecewise function h(x):
[tex]h(x)=\begin{cases}-5x-13,x<-3 \\ 5,-3\leq x<5 \\ x+1,x\ge5\end{cases}[/tex]-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
[tex]h(x)=-5x-13[/tex]Replace the expression with x=-6 and calculate the corresponding value of x:
[tex]\begin{gathered} h(-6)=-5(-6)-13 \\ h(-6)=30-13 \\ h(-6)=17 \end{gathered}[/tex]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:
[tex]h(x)=5[/tex]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:
[tex]h(0)=5[/tex]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:
[tex]h(x)=x+1[/tex]Replace the expression with x=5 and calculate the corresponding value of h(x):
[tex]\begin{gathered} h(5)=5+1 \\ h(5)=6 \end{gathered}[/tex]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:
[tex]h(x)=x+1[/tex]Replace the expression with x=9, and calculate the corresponding value of h(x):
[tex]\begin{gathered} h(9)=9+1 \\ h(9)=10 \end{gathered}[/tex]So, to sum up:
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