f(x) Transforms to |f(x)|

Q. If $f\left(x\right)=e^x,g\left(x\right)=e^x+1$ and $h\left(x\right)=e^x-1$, then which of the following is/are correct?

1. If we shift the graph of $f\left(x\right)$ by $1$ unit upward, we get the graph of $h\left(x\right)$
2. If we shift the graph of $f\left(x\right)$ by $1$ unit upward, we get the graph of $g\left(x\right)$
3. If we shift the graph of $f\left(x\right)$ by $1$ unit downward, we get the graph of $h\left(x\right)$
4. If we shift the graph of $f\left(x\right)$ by $1$ unit downward, we get the graph of $g\left(x\right)$

Q. $\text{If}f\left(x\right)=\text{max}|2\sin y-x|\text{(where}y\in R),\text{then minimum value of}f(x)\text{is}$

Q.

Draw the graph of logarithm function y= ${\log }_{a}x$ when x>0and 0<a<1.

1. 

2. 

3. 

4. 

Q. Select the correct graph of $|4\cos x-3|.$

1. 
2. 

Q. If $f\left(x\right)=|x|,g\left(x\right)=|x-2|$ and $h\left(x\right)=|x+2|$, then which of the following is/are correct?

1. If we shift the graph of $f\left(x\right)$ by $2$ units right, we get the graph of $h\left(x\right)$
2. If we shift the graph of $f\left(x\right)$ by $2$ units right, we get the graph of $g\left(x\right)$
3. If we shift the graph of $f\left(x\right)$ by $2$ units left, we get the graph of $g\left(x\right)$
4. If we shift the graph of $f\left(x\right)$ by $2$ units left, we get the graph of $h\left(x\right)$

Q. Which among the following graph(s) represents an odd function?

1. 
2. 
3. 
4. 

Q. $\text{If}f\left(x\right)=\text{max}|2\sin y-x|\text{(where}y\in R),\text{then minimum value of}f(x)\text{is}$

Q. Match the following functions and their graph

Function	Graph
1) y = |sinx|	A)
2) y = sin |x|	B)
3) |y| = sinx	C)

1. 1 - A, 2 - B, 3 - C
2. 1 - C, 2 - B, 3 - A
3. 1 - B, 2 - C, 3 - A
4. 1 - C, 2 - A, 3 - B

Q. If $f\left(x\right)=\cos x-1,$ then select the correct graph of $|f\left(x\right)|.$

1. 
2. 
3. 

Q. The function $y=\ln \left(\right|x\left|\right)$ is symmetric about y-axis.

1. True
2. False

Q. The function $y=f\left(\right|x\left|\right)$ is symmetric about the line

1. $x=0$
2. $y=0$
3. $y=x$
4. $y=-x$

Q. How to plot a graph using sine function?

Q. If (x, y) is a point on the graph of an odd function, then (-x, -y) will also be point on the same graph.

1. True
2. False

Q.

Which of the following is the graph of $y=|x-2|$

1. 

2. 

3. 

4. 

Q. If $f\left(x\right)=\cos x-1,$ then select the correct graph of $|f\left(x\right)|.$

1. 
2. 
3. 

Q.

The point in the graph of $y=x^2-2x+3$ where it attains the minimum value is

1. (2, 3)

2. (1, 2)

3. (1, 3)

4. (–1, –3)

Q. Let the function $f\left(x\right)=\{\begin{array}{cc}{\sin }^{-1}x,& -1\le x\le 1\\ a-(x-1{)}^2,& x>1\end{array}$ has a point of local maxima at $x=1,$ then the minimum value of $\frac{\pi }{a}(a>0)$ is

Q. The function $y=f\left(\right|x\left|\right)$ is symmetric about the line

1. $x=0$
2. $y=0$
3. $y=x$
4. $y=-x$

Q.

Identify the graph of $-|-x+3|$

1. 

2. 

3. 

4. 

Q.

Which of the following is the graph of $y=|x-2|$

1. 

2. 

3. 

4. 

Q. Let the function $f\left(x\right)=\{\begin{array}{cc}{\sin }^{-1}x,& -1\le x\le 1\\ a-(x-1{)}^2,& x>1\end{array}$ has a point of local maxima at $x=1,$ then the minimum value of $\frac{\pi }{a}(a>0)$ is

Q.

Identify the graph of $-|-x+3|$

1. 

2. 

3. 

4. 

Q. If (x, y) is a point on the graph of an odd function, then (-x, -y) will also be point on the same graph.

1. True
2. False

Q. $\text{If}f\left(x\right)=\text{max}|2\sin y-x|\text{(where}y\in R),\text{then minimum value of}f(x)\text{is}$

Q. The curve $\left|y\right|=x-1$is symmetric about x-axis.

1. True
2. False

Q. The function $y=\ln \left(\right|x\left|\right)$ is symmetric about y-axis.

1. True
2. False

Q. $\text{If}f\left(x\right)=\text{max}|2\sin y-x|\text{(where}y\in R),\text{then minimum value of}f(x)\text{is}$