Using Graph to Find Range of a Function

Define signum function draw its graph and find its domain and range

What are maxima and minima?

The function $f\left(x\right)=2\left|x\right|+|x+2|-||x+2|-2\left|x\right||$
has a local minimum or a local maximum at x=

1. -2

2. $\frac{-2}{3}$

3. 2

4. $\frac{2}{3}$

1. $[2,\infty )$
2. $[3,\infty )$
3. $[4,\infty )$
4. $[5,\infty )$

It is a continuous function $f$ defined on the real line $R$, assume positive and negative values in $R$ then the equation $f\left(x\right)=0$ has root in $R$. For example, if it is known that a continuous function $f$ on $R$ is positive at some point and its minimum value is negative then the equation$f\left(x\right)=0$ has a root in $R$. Consider$f\left(x\right)=k{e}^x–x$ for all real $x$ where$k$ is a real constant.The line $y=x$ meets $y=k{e}^x$ for $k\le 0$ at

1. No point

2. One point

3. Two points

4. More than two points

1. $[0,\frac{1}{2})$
2. $[0,\frac{1}{2}]$
3. $(0,1)$
4. $[0,1]$

If $f\left(x\right)=\left|x-2\right|$, where $x$ is a real number, then, which one of the following is correct?

1. $f$ is periodic

2. $f\left(x+y\right)=f\left(x\right)+f\left(y\right)$

3. $f$ is an odd function

4. $f$ is not one-one function

5. $f$ is an even function

1. $\{-1,1\}$
2. $\left\{0\right\}$
3. $[-1,1]$
4. $\left\{1\right\}$

1. $\{3,-3\}$
2. $R-\{-3\}$
3. $\{-1,1\}$
4. All positive integers

1. A
2. E and F
3. F
4. C