Answer:
The table in the attached figure
Step-by-step explanation:
we have
[tex]h(x)=\sqrt[3]{-x+2}[/tex]
Using a graphing tool
see the attached figure
The x-intercept of the function is the point [tex](2,0)[/tex] (value of x when the value of the function is equal to zero)
The y-intercept of the function is the point [tex](0,1.26)[/tex] (value of the function when the value of x is equal to zero)
therefore
First table
The y-intercept of the function is the point [tex](0,2)[/tex]
so
Is not represent the function h(x)
Second table
The y-intercept of the function is the point [tex](0,2)[/tex]
so
Is not represent the function h(x)
Third table
The x-intercept of the function is the point [tex](2,0)[/tex]
so
Could be represent the function h(x)
Fourth table
The x-intercept of the function is the point [tex](-2,0)[/tex]
so
Is not represent the function h(x)
Verify the third table
For [tex]x=-6[/tex]
Find the value of y
substitute the value of x
[tex]h(-6)=\sqrt[3]{-(-6)+2}=2[/tex] -----> is ok
For [tex]x=1[/tex]
Find the value of y
substitute the value of x
[tex]h(1)=\sqrt[3]{-(1)+2}=1[/tex] -----> is ok
For [tex]x=3[/tex]
Find the value of y
substitute the value of x
[tex]h(3)=\sqrt[3]{-(3)+2}=-1[/tex] -----> is ok
For [tex]x=10[/tex]
Find the value of y
substitute the value of x
[tex]h(10)=\sqrt[3]{-(10)+2}=-2[/tex] -----> is ok
The third table represent the function h(x) ------> see the attached figure
