Begin by graphing f(x)=log_{2}x Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. r(x)=log_{2}(-x)

${\displaystyle {\sec }^2\left(x\right)-1=0}$

The two linear equations shown below are said to be dependent and consistent: $2x-5y=3$
$6x-15y=9$
Explain in algebraic and graphical terms what happens when two linear equations are dependent and consistent.

g(x)
${\displaystyle =\frac{2x^2-3x-20}{x-4},\text{if}x\ne 4}$
and
=kx-15, if x=4
Evaluate the constant k that makes the function continuous.

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
${\displaystyle h\left(x\right)=-\surd x+1+9}$

Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each functions

Prove that V is a vector space. ${\displaystyle V=T(m,n)}$, the set of linear transformations ${\displaystyle T:R^m\to R^n}$, together with the usual addition and scalar multiplication of functions.

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) ${\displaystyle f\left(x\right)=\log (-\left(\frac{1}{3}\right)x)-3}$