Find the equation of each graph after the given transformation.

(g) $y=x^2+x$ after translation by $\left(\begin{array}{c}-1\\ 0\end{array}\right)$.

Find the equation of each graph after the given transformation.

(h) $y=3x^2-2$ after translation by $\left(\begin{array}{l}2\\ 3\end{array}\right)$.

Find the translation that transforms the graph.

(a) $y=x^2+5x-2$ to the graph $y=x^2+5x+2$.

Find the translation that transforms the graph.

(b) $y=x^3+2x^2+1$ to the graph $y=x^3+2x^2-4$.

Find the translation that transforms the graph.

(c) $y=x^2-3x$ to the graph $y=(x+1{)}^2-3(x+1)$.

Find the translation that transforms the graph.

(d) $y=x+\frac{6}{x}$ to the graph $y=x-2+\frac{6}{x-2}$.

Find the translation that transforms the graph.

(e) $y=\sqrt{2x+5}$ to the graph $y=\sqrt{2x+3}$.

Find the translation that transforms the graph.

(f) $y=\frac{5}{x^2}-3x$ to the graph $y=\frac{5}{(x-2{)}^2}-3x+10$.
 

The diagram shows the graph of $y=f\left(x\right)$. Sketch the graphs of each of the following functions.

(a) $y=f\left(x\right)-4$.