QuestionWhat happens to the values of $f(x)=x^{3}+5$ compared to $y=x^{3}$? How does this change affect the graph?

Studdy Solution
To visualize this, consider the point (2,8) on the graph of $y = x^{3}$.
After adding5 to the function, the corresponding point on the graph of $f(x) = x^{3} +5$ is (2,13), which is5 units above the point (2,8).
So, the graph of $f(x) = x^{3} +5$ is the graph of $y = x^{3}$ shifted upward by5 units.
In conclusion, adding5 to the function $y = x^{3}$ increases the function's values by5 for any given $x$, and shifts the graph of the function upward by5 units.