Modulus Function

Q.

Question 110

Solve the following

For what value of x is the perimeter of shape 77 cm?

Q. If $A=\{x:4<3x-2\le 13,xϵR\}$ and $B=\{x:-2\le 5+7x<40,xϵI\}$, then write down the element of $A\cap B$.
[4 MARKS]

Q.

Which of the following are the graphs of odd functions?

1. 

2. 

3. 

4. 

Q.

Mention the procedures to draw the quadratic graph $y=a{x}^2+bx+c$

Q. Draw the graph $y=|x+2|+|x-3|$.

Q. The graph obtained by plotting $y=x^2$ is in the shape of a ___ .

Q. Draw the graph of function $f:R\to R$ defined by $f\left(x\right)=\left|x-2\right|$ . Also write its domain and Range.

Q. For the smallest positive values of 'x' and 'y' the equation $2(sinx+siny)-2cos(x-y)=3$ has a solution then which of the following is/are true

1. $sin\left(\frac{x+y}{2}\right)=1$
2. $cos\left(\frac{x-y}{2}\right)=\frac{1}{2}$
3. Number of ordered pairs (x, y) is 2
4. Number of ordered pairs (x, y) is 3

Q. If $f\left(x\right)=(1+\sin \frac{\pi }{8x})(1-\sin \frac{(4x-1)\pi }{8x})(1+\sin \frac{(4x+1)\pi }{8x})(1-\sin \frac{(8x-1)\pi }{8x})$ then

1. $\underset{x\to 0}{lim}{x}^{2}f\left(x\right)=\frac{{\pi }^2}{16}$
2. For $f\left(x\right)=0$, the largest positive solution of $x$ is $\frac{1}{4}$
3. $f\left(2\right)=\frac{1}{8}(2-\sqrt{2})$
4. $f\left(x\right)$ is a even function

Q. The number of solution of the equation ${\left|x\right|}^2+|x-3|+a=0$; where $a=\{\begin{array}{c}-3,ifx\ge 3\\ -\frac{11}{4},ifx<3\end{array}$ is -

1. $1$
2. $2$
3. $3$
4. $4$

Q. The domain of the function, f = {(1, 2), (2, 3), (4, 5)} is ______.

1. {2, 3, 5}
2. {1, 2, 5}
3. {1, 2, 3}
4. {1, 2, 4}

Q. The minimum value of $f\left(x\right)=|x-1|+|x-2|+|x-3|$ is equal to

1. $1$
2. $2$
3. $3$
4. $0$

Q. Find the values of $x$ satisfying the equation
$|x^2-9|+|x^2-1|+|x^2-5x+6|=0$

Q. Which of the following represents the vertex of the curve obtained by plotting $y=2x^2$?

1. (1, -4)
2. (0, 1)
3. (0, 0)
4. (1, 0)

Q. (x^2-5)(x^2-4)/(x-1) what will be the inequality of this?

Q. Draw the graph of $|x|+|y|+|x+y|=1$.

Q. Find the domain of the function.

1. R - {-1}
2. R - {0}
3. R - {-3}
4. R - {-2}

Q. If the graph of $y=\mid x\mid$ is shifted to the right by $a$, we get the graph of?

1. $y=\mid x+a\mid$
2. $y=\mid x-a\mid$
3. $y=\mid \frac{x}{a}\mid$
4. $y=\mid x\mid +a$

Q. Draw graph of $f:R\to R,$ $f\left(x\right)=\left|x\right|$

Q. How do you solve $\sin x+\cos x=0$?

Q. Construct the graphs of the following functions.
$y=(|x+1|-|x-1|)/2.$

Q. Graph of $y=|2-x^2|$

Q. Define modulus function. Draw the graph of Modulus function and writes its Domain and range.

Q.

If f : R$\to$ R is a function defined by

$f\left(x\right)=\{\begin{array}{c}2x\text{if}x⩾0\\ -3x\text{if}x<0\end{array}$

Find the value of f(-10).f(2) + f(-1) – f(3).

Q. Draw a graph for the function:
$y=x+\left|x\right|$

Q. Draw graph of the function $f\left(x\right)=|x+2|$ and determine at which point does the graph intersect $x$-axis.

1. $(2,0)$
2. $(0,0)$
3. $(-2,0)$
4. Never intersect $x$-axis

Q. Solve each of the following system of equations graphically:
$x+2y+2=0$
$3x+2y-2=0$

Q. The maximum number of values of $x$ if $|x-2|+|x-4|=2$ is

1. $1$
2. $2$
3. $3$
4. Infinitely many

Q. Draw the graph of the following function: $f\left(x\right)=|x-2|+|x-3|$

Q. Construct the graphs of the following functions.
$y=x^2-2|x|+1-1.$