Demystify College Algebra with Step-by-Step Examples and Expert Guidance

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.

$\begin{array}{|ccccccccccc|}\hline x& 4& 5& 6& 7& 8& 9& 10& 11& 12& 13\\ f(x)& 9.429& 9.972& 10.415& 10.79& 11.115& 11.401& 11.657& 11.889& 12.101& 12.295\\ \hline\end{array}$

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic. $\begin{array}{|ccccccccccc|}\hline x& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ f\left(x\right)& 3.05& 4.42& 6.4& 9.28& 13.46& 19.52& 28.3& 41.04& 59.5& 86.28\\ \hline\end{array}$

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f (x).

$\begin{array}{|cccccc|}\hline x& -2& -1& 0& 1& 2\\ f(x)& -1& -3& 4& 2& 1\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline x& -3& -2& -1& 0& 1\\ g(x)& -1& -3& 4& 2& 1\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline x& -2& -1& 0& 1& 2\\ h(x)& -2& -4& 3& 1& 0\\ \hline\end{array}$

Sketch a graph of the function. Use transformations of functions whenever possible.
$f(x)=\{\begin{array}{lll}1-x& if& x<0\\ 1& if& x\ge 0\end{array}$

$f:R->R$
$f(x)=8x-2$
$f(a)=f(b)$
${\displaystyle a,b\in R}$
Prove that f is one-to-one.

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x).

$\begin{array}{|cccccc|}\hline x& -2& -1& 0& 1& 2\\ f(x)& -2& -1& -3& 1& 2\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline x& -1& 0& 1& 2& 3\\ g(x)& -2& -1& -3& 1& 2\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline x& -2& -1& 0& 1& 2\\ h(x)& -1& 0& -2& 2& 3\\ \hline\end{array}$

The function g is related to one of the parent functions described in an earlier section.
${\displaystyle g\left(x\right)=\frac{1}{6}\sqrt{x}}$
a) Identify the parent function f.
b)Describe the sequence of transformations from f to g.
c)Use function notation to write g in terms of f.
$g(x)=(?)f(x)$