Sue Pemberton Solutions for Chapter: Functions, Exercise 10: EXERCISE 2H

Determine the sequence of transformations that maps:

(b) The curve $y=x^3$ onto the curve $y=-\frac{1}{2}(x+1{)}^3-2$.

Determine the sequence of transformations that maps:

(c) The curve $y=\sqrt[3]{x}$ onto the curve $y=-2\sqrt[3]{x-3}+4$.

Given that $f\left(x\right)=\sqrt{x}$, write down the equation of the image of $f\left(x\right)$ after:

(a) Reflection in the $x$ -axis, followed by translation $\left(\begin{array}{l}0\\ 3\end{array}\right)$, followed by translation $\left(\begin{array}{l}1\\ 0\end{array}\right)$, followed by a stretch parallel to the $x$ -axis with stretch factor 2.

Given that $f\left(x\right)=\sqrt{x}$, write down the equation of the image of $f\left(x\right)$ after:

(b) Translation $\left(\begin{array}{l}0\\ 3\end{array}\right)$, followed by a stretch parallel to the $x$ -axis with stretch factor 2, followed by a reflection in the $x$ -axis, followed by translation $\left(\begin{array}{l}1\\ 0\end{array}\right)$.

Given that $g\left(x\right)=x^2$, write down the equation of the image of $g\left(x\right)$ after:

(a) Translation $\left(\begin{array}{r}-4\\ 0\end{array}\right)$, followed by a reflection in the $y$ -axis, followed by translation $\left(\begin{array}{l}0\\ 2\end{array}\right)$. followed by a stretch parallel to the $y$ -axis with stretch factor 3.

Given that $g\left(x\right)=x^2$, write down the equation of the image of $g\left(x\right)$ after:

(b) A stretch parallel to the $y$ -axis with stretch factor 3, followed by translation $\left(\begin{array}{l}0\\ 2\end{array}\right)$, followed by reflection in the $y$ -axis, followed by translation $\left(\begin{array}{c}-4\\ 0\end{array}\right)$.

Find two different ways of describing the combination of transformations that maps the graph of $f\left(x\right)=\sqrt{x}$ onto the graph $g\left(x\right)=\sqrt{-x-2}$ and sketch the graphs of $y=\mathrm{f}\left(x\right)$ and $y=\mathrm{g}\left(x\right)$.

Find two different ways of describing the sequence of transformations that maps the graph of $y=f\left(x\right)$ onto the graph of $y=f(2 x+10)$.