SOLUTION:
Case: Shifting a graph
The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down. Here are the graphs of y = f (x), y = f (x) + 2, and y = f (x) - 2
Given:
[tex]\begin{gathered} y=x^3 \\ shifting\text{ 8 units up} \end{gathered}[/tex]
Required:
To show how the function changes
Method:
Step 1:
The original function
[tex]y=x^3[/tex]
At the original function, the graph cuts through (0,0).
Step 2:
When it is shifted 8 units up, the graph will now cut through (0,8).
The function will now be:
[tex]y=x^3+8[/tex]
Final answer:
[tex]y=x^3+8[/tex]
