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

Table shows the number of wireless service subscribers in the United States and their average monthly bill in the years from 2000 through 2015

. $\begin{array}{ccc}\text{Year}& \text{Subscribers}& \text{Average Monthly}\\ & \text{(millions)}& \text{Revenue per Subscriber Unit }\\ \text{2000}& \text{109.5}& \text{48.55}\\ \text{2001}& \text{128.4}& \text{49.79}\\ \text{2002}& \text{140.8}& \text{51.00}\\ \text{2003}& \text{158.7}& \text{51.55}\\ \text{2004}& \text{182.1}& \text{52.54}\\ \text{2005}& \text{207.9}& \text{50.65}\\ \text{2006}& \text{233.0}& \text{49.07}\\ \text{2007}& \text{255.4}& \text{49.26}\\ \text{2008}& \text{270.3}& \text{48.87}\\ \text{2009}& \text{285.6}& \text{47.97}\\ \text{2010}& \text{296.3}& \text{47.53}\\ \text{2011}& \text{316.0}& \text{46.11}\\ \text{2012}& \text{326.5}& \text{48.99}\\ \text{2013}& \text{335.7}& \text{48.79}\\ \text{2014}& \text{355.4}& \text{46.64}\\ \text{2015}& \text{377.9}& \text{44.65}\end{array}$

One of the scatter plots suggests a linear model. Use the points at t = 0 and t = 15 to find a model in the form y = mx + b.

A simplified form of $(\sqrt{3^{2}x})+2+3^{-2x}$ that does not involve radicals or fractional exponents can be obtained after factoring the radicand. Find this simplification.

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x). $\overline{)\begin{array}{c}\\ x& -2& -1& 0& 1& 2\\ \\ f(x)& -2& -1& -3& 1& 2\end{array}}$

$\overline{)\begin{array}{c}\\ x& -1& 0& 1& 2& 3\\ g(x)& -2& -1& -3& 1& 2\end{array}}$

$\overline{)\begin{array}{c}\\ x& -2& -1& 0& 1& 2\\ h(x)& -1& 0& -2& 2& 3\end{array}}$

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
${\displaystyle h\left(x\right)=-\sqrt{x+4}}$

${\displaystyle 4\sqrt{x}+x=1}$

Describe the transformations that must be applied to the parent function to obtain each of the following functions.
a) ${\displaystyle f\left(x\right)=-3\log \left(2x\right)}$
b) ${\displaystyle f\left(x\right)=\log (x-5)+2}$
c) ${\displaystyle f\left(x\right)=\left(\frac{1}{2}\right)\log 5x}$
d) ${\displaystyle f\left(x\right)=\log (-\left(\frac{1}{3}\right)x)-3}$

Use the given graph of f to find a number $\delta$ such that if $|x-1|<\delta$ then $|f(x)-1|<0.2$
$\delta =?$

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
$h(x)=|x+3|-5.$

h is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to h. (c) Sketch the graph of h by hand. (d) Use function notation to write h in terms of the parent function f. ${\displaystyle h\left(x\right)=\mid 2x+8\mid -1}$

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f. ${\displaystyle g\left(x\right)=\frac{1}{2}\mid x-2\mid -3}$