Given the function below
[tex]f(x)=2(x-3)^3+1[/tex]
To create a table of values
For the range of values of x from -2 to 2
Where x = -2
[tex]\begin{gathered} f(x)=2(x-3)^3+1 \\ f(-2)=2(-2-3)^3+1=2(-5)^3+1=2(-125)+1=-250+1=-249 \\ f(-2)=-249 \end{gathered}[/tex]
Where x = -1
[tex]\begin{gathered} f(x)=2(x-3)^3+1 \\ f(-1)=2(-1-3)^3+1=2(-4)^3+1=2(-64)+1=-128+1=-127 \\ f(-1)=-127 \end{gathered}[/tex]
Where x = 0
[tex]\begin{gathered} f(x)=2(x-3)^3+1 \\ f(0)=2(0-3)^3=2(-27)+1=-54+1=-53 \\ f(0)=-53 \end{gathered}[/tex]
Where x = 1
[tex]\begin{gathered} f(x)=2(x-3)^3+1 \\ f(1)=2(1-3)^3+1=2(-2)^3+1=2(-8)+1=-16+1=-15 \\ f(1)=-15 \end{gathered}[/tex]
Where x = 2
[tex]\begin{gathered} f(x)=2(x-3)^3+1 \\ f(2)=2(2-3)^3+1=2(-1)^3+1=2(-1)+1=-2+1=-1 \\ f(2)=-1 \end{gathered}[/tex]
The table of values is shown below
The graph of the given function is shown below
