Properties of Functions

Find the domain of

 $f\left(x\right)=\frac{x-3}{\sqrt{4x-3}}$  

•  $\left(-\infty,\ \frac{3}{4}\right)\cup\left(\frac{3}{4},\infty\right)$  

•  $\left[\frac{3}{4},\ \infty\right)$  

•  $\left(\frac{3}{4},\infty\right)$  

•  $\left[\frac{3}{4},\ 3\right)\cup\left(3,\ \infty\right)$  

Find the domain of

 $g\left(x\right)=\frac{x+1}{x^2+9}$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(-\infty,-3\right)\cup\left(-3,3\right)\cup\left(3,\infty\right)$  

•  $\left(3,\infty\right)$  

•  $\left(-\infty,\ 3\right)\cup\left(3,\infty\right)$  

Find the domain of

 $h\left(x\right)=\frac{\sqrt{2-x}}{x}$  

•  $\left(-\infty,0\right)\cup\left(0,2\right)\cup\left(2,\infty\right)$  

•  $\left(-\infty,0\right)\cup\left(0,\infty\right)$  

•  $\left[2,\ \infty\right)$  

•  $\left(-\infty,0\right)\cup\left(0,2\right]$  

•  $\left(-\infty,2\right]$  

Find the zero of the function

 $f\left(x\right)=\frac{2x-5}{x-3}$  

Over what interval(s) in the function increasing?

• $\left(-\infty,1\right)$

• $\left(-\infty,5\right)$

• $\left(-\infty,\infty\right)$

• ( $\left(-\infty,1\right)\cup\left(5,\infty\right)$

Which of the following represent functions?

• $\left\{\left(x,y\right):\ \ 2x-3y=10\right\}$

• $\left\{\left(x,y\right):\ x+5=3\right\}$

• $\left\{\left(x,y\right):\ x^2+y^2=4\right\}$

• $\left\{\left(x,y\right):\ y=\left|x-3\right|\right\}$

• $\left\{\left(x,y\right):\ \ xy-y=6\right\}$

What is

 $f\left(2\right)$  ?

For which value(s) of x does

 $f\left(x\right)=1$  

•  $2.5$  

•  $-6$  

•  $-2$  

•  $5$  

Over which intervals is the function decreasing?

• $\left(3,2\right)\cup\left(4,-\infty\right)$

• $\left(-4,-2\right)\cup\left(4,\infty\right)$

• $\left(-4,\ \infty\right)$

• $\left(-\infty,\infty\right)$

Select any relative maximum of the function.

• $\left(-4,3\right)$

• $\left(-2,1\right)$

• $\left(4,4\right)$

• There are no relative maximum points.