Changing Graphs

The following star shape (A) is created by connecting the following points in the order given : $(1,1), (2,2), (1,2), (2,0.5), (1.5,2.5)$ and back to $\left(1, 1\right)$

Fully describe the transformation of star from A to B.

Here is the graph of $y={\left(x-2\right)}^2+3$. Find the equations of graph $A \text{and} B$.

This diagram shows an example of graph transformations. Describe the transformations applied to map the blue curve onto the red curve.

Define plane transformation.

Define transformations. State which combination of transformations has been applied to $f\left(x\right)$ to get $g\left(x\right): f\left(x\right)=x^2+4x+4, g\left(x\right)=x^2-5$.

If $f\left(x\right)=e^x$ and $g\left(x\right)=lnx,$ then the number of positive real solutions of $f\left(–\left|x\right|\right)=g\left(\left|x\right|\right)$ is

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

Cotyledons are also called-

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