True or False: For the function $f(x)=x^3$, the transformation $y=-f(x)$ results in the same graph as $y=f(-x)$.

Which of the following describes the vertical translation applied to the function $y=(x+1{)}^2$ to obtain the graph of $y=x^2+2x+5$?

A function $f(x)$ is defined by the set of points: $$\{(-4,-5),(1,-1),(5,3)\}$$ If $g(x)=\frac{1}{2}f(x)$, which of the following represents the transformed set of points on the graph of $g$?

True or False: If $f(x)$ is a linear function with equation $y=mx+c$ (where $m\ne 0$), then for any vertical translation $k\ne 0$, the graph of $g(x)=f(x)+k$ will be parallel to and never intersect the graph of $f(x)$.

If the graph of $$y=f(x)$$ is translated vertically by $$k$$ units such that the resulting graph is identical to the original graph (i.e., $$f(x)+k=f(x)$$ for all $$x$$), what must be the value of $$k$$?