a.

$x$	$f\left(x\right)=2x+1$	$g\left(x\right)=-f\left(x\right)$	$h\left(x\right)=f\left(-x\right)$
$-4$	$-7$	$7$	$9$
$-2$	$-3$	$3$	$5$
$0$	$1$	$-1$	$1$
$2$	$5$	$-5$	$-3$
$4$	$9$	$-9$	$-7$

b.

c.

The points on $g\left(x\right)$ have the same $x$-values as $f\left(x\right)$, but the $y$-values have opposite signs. There is an invariant point on the $x$-axis at $\left(-0\mathrm{.}5\mathrm{,}0\right)$.
The points on $h\left(x\right)$ have the same $y$-values as $f\left(x\right)$, but the $x$-values have opposite signs. There is an invariant point on the $y$-axis at $\left(0\mathrm{,}1\right)$.

d.

The graph of $g\left(x\right)$ is a reflection of $f\left(x\right)$ in the $x$-axis. The graph of $h\left(x\right)$ is a reflection of $f\left(x\right)$ in the $y$-axis.

a.

b.

c.

The points on $g\left(x\right)$ have the same $x$-values as $f\left(x\right)$, but the $y$-values have been multiplied by $3$.
The point $\left(0\mathrm{,}0\right)$ is invariant.
The points on $h\left(x\right)$ have the same $x$-values, but the $y$-values have been multiplied by $\frac{1}{3}$.
The point $\left(0\mathrm{,}0\right)$ is invariant.

d.

The graph of $g\left(x\right)$ is a vertical stretch about the $x$-axis of $f\left(x\right)$ by a factor of $3$. The graph of $h\left(x\right)$ is a vertical stretch about the $x$-axis of $f\left(x\right)$ by a factor of $\frac{1}{3}$.

a.

The equation of the reflected function is $g\left(x\right)=-3x$.

The domain is $\left\{x\mid x\in \mathrm{R}\right\}$ and the range is $\left\{y\mid y\in \mathrm{R}\right\}$ for both functions.

b.

The equation of the reflected function is


The domain of $g\left(x\right)$ is $\left\{x\mid x\in \mathrm{R}\right\}$ and the range is $\left\{y\mid y\ge 1\mathrm{,}y\in \mathrm{R}\right\}$.

The domain of $h\left(x\right)$ is $\left\{x\mid x\in \mathrm{R}\right\}$ and the range is $\left\{y\mid y\le -1\mathrm{,}y\in \mathrm{R}\right\}$.

c.

The equation of the reflected function is


The domain of $h\left(x\right)$ is $\left\{x\mid x\ne 0\mathrm{,}x\in \mathrm{R}\right\}$ and the range is $\left\{y\mid y\ne 0\mathrm{,}y\in \mathrm{R}\right\}$.

The domain of $k\left(x\right)$ is $\left\{x\mid x\ne 0\mathrm{,}x\in \mathrm{R}\right\}$ and the range is $\left\{x\mid x\ne 0\mathrm{,}y\in \mathrm{R}\right\}$.

a.

The domain of the transformed function is $\left\{x\mid -6\le x\le 6x\in \mathrm{R}\right\}$. The range is $\left\{y\mid -8\le y\le 8\mathrm{,}y\in \mathrm{R}\right\}$.

b.

The vertical stretch increased the range by a factor of $2$. The domain was not changed.

a.

b.

The graph of function $f\left(x\right)$ has been reflected in the $x$-axis.

c.

The graph of function $f\left(x\right)$ has been stretched horizontally about the $y$-axis by a factor of $\frac{1}{3}$.

d.

The graph of function $f\left(x\right)$ has been reflected in the $y$-axis.

a.

b.

c.

The order does not matter because both produced the same graph. Neither person is correct.