Transformation of Graphs

Graph $f\left(x\right) = 6 \sqrt{(9 – x^2)}$ by finding its intercepts. On the same coordinate system, graph g(x) with the following conditions:

The function g(x) is the result of f(x) being vertically compressed by a factor of $\frac{1}{2}$.

The number of real solutions of the ${\log }_{0.5}\left|x\right|=2\left|x\right|$ is:

If equation $x^2-4\left|x\right|+k=0$ has $4$ distinct real roots, then values of $k$ can be :

Consider the equation $\mathrm{sin\pi }x-{\log }_e\left|x\right|=0$, then which of the following are CORRECT?

Which of the following is/are correct?

Number of solution(s) of the equation ${\sin }^{-1}\left|x\right|=\left|{\cos }^{-1}x\right|$, is/are

The equation of image of pair of lines $y=\left|x-1\right|$ in y-axis is

If the graph $y=f\left(x\right)$ is symmetrical about the lines $x=1$ and $x=2,$ then which of the following is true

Graphical representation of different functions is also a method to find the number of solution(s) of any equation. The number of solution of the equation $f_1\left(x\right)=f_2\left(x\right)$ is equal to the number of points of intersection of the graphs of $y=f_1\left(x\right)$ and $y=f_2\left(x\right)$. Now consider the equation $\left|x-1\right|+\left|x-2\right|+\left|x-3\right|=k$. If $k>2$, then number of solutions of the equation is

Graphical representation of different functions is also a method to find the number of solution(s) of any equation. The number of solution of the equation $f_1\left(x\right)=f_2\left(x\right)$ is equal to the number of points of intersection of the graphs of $y=f_1\left(x\right)$ and $y=f_2$ . Now consider the equation $\left|x-1\right|+\left|x-2\right|+\left|x-3\right|=k,$ and give the answers of t he following questions.

If $k=2$ , then number of solutions of the equation is

If the pressure $P$ and volume $V$ of a gas are related by the equation $P{V}^{\gamma }=\text{constant},$ where $\mathrm{\gamma }$ is a positive constant. Then the graph of $\frac{\left(\frac{dP}{dV}\right)}{P}$versus $V$ will be:

The graph of $y=f\left(x\right)$ is symmetrical about the line $x=1$, then

The graph of $y=f\left(x\right)$ is symmetrical about the line $x=1$, then

If the function $f\left(x\right)=\left|x^2+a\left|x\right|+b\right|$ has exactly three points of non-differentiability, then which of the following may hold:

$f\left(x\right)=\{\begin{array}{ccc}2-x^2-x& ;& x\in \left[-1, 0\right]\\ 2& ; & x\in \left(-\infty , -1\right)\cup (0, 1]\\ x+1& ;& x\in [1,\infty )\end{array}$

, then range of $g\left(x\right)$ is

Suppose $f: [-2, 2]\to R$ is defined by $f\left(x\right)=\left\{\begin{array}{c}-1, \mathrm{for} -2\le x\le 0\\ x-1, \mathrm{for} 0\le x\le 2\end{array}\right.$, then $\{x\in \left[-2,2\right]:x\le 0 \text{and} f(\left|x\right|)=x\}$ is equal to

Number of solutions of $y=e^x$ and $y=\sin x$ is