함수의 뜻

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.

$f(x)=\{\begin{array}{ccc}3 & \text{if} & x<0 \\ \sqrt{x} & \text{if} & x\ge 0\end{array}$

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.

$$f(x)=\{\begin{array}{c}{x}^{2}\,\text{ if }x<0 \\ 1-x\,\text{ if }x>0\end{array}$$

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.

$f(x)=\{\begin{array}{c}\begin{array}{c}{x}^{2} \\ x+2\end{array}\end{array}\,\,\begin{array}{c}\text{if}\,\,\,\,\,x<0 \\ \text{if}\,\,\,\,\,x\ge 0\end{array}$

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.

$f(x)=\{\begin{array}{ccc}x+1 & \text{if} & x<1 \\ {x}^{3} & \text{if} & x\ge 1\end{array}$

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.

$f(x)=\{\begin{array}{c}|x| \\ 1\end{array}\begin{array}{c}\,\,\,\text{if}\,\,\,x<2 \\ \,\,\,\text{if}\,\,\,x\ge 2\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-3),\,f(-2),\,f(-1),$ and $f(0).$

$f(x)=\{\begin{array}{ccc}x+1 & \text{if} & x<-2 \\ -2x-3 & \text{if} & x\ge -2\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-3),\,f(-2),\,f(-1),$ and $f(0).$

$f(x)=\{\begin{array}{cc}1 & \text{if }x\le -3 \\ 0 & \text{if }x>-3\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-3),\,f(-2),\,f(-1),$ and $f(0).$

$f(x)=\{\begin{array}{cc}-2{x}^{2}+3 & \text{if }x\le -1 \\ 5x-7 & \text{if }x>-1\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-1),\,f(0),\,f(2),$ and $f(4).$

$f(x)=\{\begin{array}{ccc}7x+3 & \text{if} & x<0 \\ 7x+6 & \text{if} & x\ge 0\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-1),\,f(0),\,f(2),$ and $f(4).$

$f(x)=\{\begin{array}{ccc}{x}^{2}-2 & \text{if} & x<2 \\ 4+|x-5| & \text{if} & x\ge 2\end{array}$

For the following exercises, given each function $f,$ evaluate $f(-1),\,f(0),\,f(2),$ and $f(4).$

$f(x)=\{\begin{array}{ccc}5x & \text{if} & x<0 \\ 3 & \text{if} & 0\le x\le 3 \\ {x}^{2} & \text{if} & x>3\end{array}$

For the following exercises, write the domain for the piecewise function in interval notation.

$f(x)=\{\begin{array}{c}x+1\,\text{if}\,x<-2 \\ -2x-3\,\text{if}\,x\ge -2\end{array}$

For the following exercises, write the domain for the piecewise function in interval notation.

$f(x)=\{\begin{array}{c}{x}^{2}-2\,\text{if}\,x<1 \\ -{x}^{2}+2\,\text{if}\,x>1\end{array}$

For the following exercises, write the domain for the piecewise function in interval notation.

$f(x)=\{\begin{array}{c}2x-3 \\ -3{x}^{2}\end{array}\,\begin{array}{c}\text{if}\,x<0 \\ \text{if}\,x\ge 2\end{array}$

Graph $y=\frac{1}{{x}^{2}}$ on the viewing window $[-0.5,-0.1]$ and $[0.1,0.5].$ Determine the corresponding range for the viewing window. Show the graphs.

Graph $y=\frac{1}{x}$ on the viewing window $[-0.5,-0.1]$ and $[0.1,\,0.5].$ Determine the corresponding range for the viewing window. Show the graphs.

Suppose the range of a function $f$ is $[-5,\,8].$ What is the range of $|f(x)|?$

Create a function in which the range is all nonnegative real numbers.

Create a function in which the domain is $x>2.$

The height $h$ of a projectile is a function of the time $t$ it is in the air. The height in feet for $t$ seconds is given by the function $h(t)=-16{t}^{2}+96t.$ What is the domain of the function? What does the domain mean in the context of the problem?