Find the equation of each graph after the given transformation.

(a) $y=3x^2$ after a stretch parallel to the $y$ -axis with stretch factor $2$.

Find the equation of each graph after the given transformation.

(b) $y=x^3-1$ after a stretch parallel to the $y$ -axis with stretch factor $3$.

Find the equation of each graph after the given transformation.

(c) $y=2^x+4$ after a stretch parallel to the $y$ -axis with stretch factor $\frac{1}{2}$.

Find the equation of each graph after the given transformation.

(d) $y=2x^2-8x+10$ after a stretch parallel to the $x$ -axis with stretch factor $2$.

Find the equation of each graph after the given transformation.

(e) $y=6x^3-36x$ after a stretch parallel to the $x$ -axis with stretch factor $\frac{1}{3}$.

Describe the single transformation that maps the graph:

(a) $y=x^2+2x-5$ onto the graph $y=4x^2+4x-5$.

Describe the single transformation that maps the graph:

(b) $y=x^2-3x+2$ onto the graph $y=3x^2-9x+6$.

Describe the single transformation that maps the graph:

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

Describe the single transformation that maps the graph:

(d) $y=\sqrt{x-6}$ onto the graph $y=\sqrt{3x-6}$.