## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$y= x^3+4$
In order to find the answer, we will have to recall the following some point about the graph of $y=f(x)$. a) The graph of the function $y=-f(x)$ involves a reflection about the $x$-axis of the original function $f(x)$. b) The graph of the function $y=f(x)+a$ defines a vertical shift of $|a|$ units upward when $a \gt 0$, and downward side when $a\lt 0$ of the original function $f(x)$. c) The graph of $y=f(x-p)$ defines a horizontal shift of $|p|$ units to the right when $p \gt 0$, and to the left when $p \lt 0$ of the original function $f(x)$. (d) The graph of $y=k\cdot f(x)$ can be obtained a vertical stretch when $k\gt 1$ or compression when $0\lt k \lt1$) of the original function $f(x)$. As mentioned in point $(b)$ above, the resulting graph would attain a $4$-unit upward of the original function $f(x)$. So, we have new function as: $y=f(x)+a \\ y= x^3+4$