# Transformation properties questions and answers

Recent questions in Transformation properties
Transformation properties

### Find an equation of the hyperbola satisfying the indicated properties. Vertices at $$\displaystyle{\left({0},\ {1}\right)}$$ and $$\displaystyle{\left({0},\ -{1}\right)}$$. asymptotes are the lines $$\displaystyle{x}=\pm{3}{y}$$

Transformation properties

### If $$\displaystyle{f{{\left(\theta\right)}}}={\csc{\theta}}$$ and $$\displaystyle{f{{\left({a}\right)}}}={2},$$ find the exact value of: a) $$\displaystyle{f{{\left(-{a}\right)}}}$$ b) $$\displaystyle{f{{\left({a}\right)}}}+{f{{\left({a}+{2}\pi\right)}}}+{f{{\left({a}+{4}\pi\right)}}}$$

Transformation properties

### Write an equation for a sinusoidal graph with the following properties: $$\displaystyle{A}=-{3}$$ period $$\displaystyle={\frac{{{2}\pi}}{{{3}}}}$$ phase shift $$\displaystyle=-{\frac{{\pi}}{{{4}}}}$$

Transformation properties

### The coordinate $$\displaystyle{\left({x},{y}\right)}$$ is rotated CW. then translated 6 units up 2 units left, and then dilated by a scale factor of 5. The combine transformation rule based on the following transformattion.

Transformation properties

### The properties of function $$\displaystyle{f{{\left({x}\right)}}}$$ as 1) The domain of $$\displaystyle{f}$$ is $$\displaystyle{\left(-\infty,\infty\right)}$$ 2) $$\displaystyle{f{{\left({3}\right\rbrace}}}={7}$$ 3) $$\displaystyle{f}$$ is continuous st $$\displaystyle{x}={2}$$ 4) $$\displaystyle{f}$$ is not continuous at $$\displaystyle{x}={4}$$ and 5) $$\displaystyle\lim_{{{x}\rightarrow+\infty}}{f{{\left({x}\right)}}}={1}$$ To find: The equation of function $$\displaystyle{f{{\left({x}\right)}}}$$ which satisfies all given properties.

Transformation properties

### Evaluate Definite Integral Using Integral Properties: If $$\displaystyle{\int_{{{1}}}^{{{7}}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}={2.5}$$ and $$\displaystyle{\int_{{{1}}}^{{{7}}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}={4}$$, find $$\displaystyle{\int_{{{1}}}^{{{7}}}}{\left[{4}{f{{\left({x}\right)}}}-{2}{g{{\left({x}\right)}}}\right]}{\left.{d}{x}\right.}$$.

Transformation properties

### Explain how to find the value of sin $$\displaystyle{390}^{{\circ}}$$ using periodic properties.

Transformation properties

### If $$\displaystyle{a},{b},{c},{d}$$ are in continued properties, prove that $$\displaystyle{\frac{{{\left({a}-{b}\right)}^{{{3}}}}}{{{\left({b}-{c}\right)}^{{{3}}}}}}={\frac{{{a}}}{{{d}}}}$$

Transformation properties

### Explain how to find the value of $$\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}$$ using even-odd properties.

Transformation properties

### Expand using logarithmic properties. Where possible, evaluate logarithmic expressions. $$\displaystyle{{\log}_{{{5}}}{\left({\frac{{{x}^{{{3}}}\sqrt{{{y}}}}}{{{125}}}}\right)}}$$

Transformation properties

### Determine whether the following series converge or diverge using the properties. $$\displaystyle{\sum_{{{k}={0}}}^{{\infty}}}{\frac{{{10}}}{{{k}^{{{2}}}+{9}}}}$$

Transformation properties

### Designer functions Design a sine function with the given properties. NKS It has a period of 12 hr with a minimum value of $$\displaystyle-{4}$$ at $$\displaystyle{t}={0}$$ hr and a maximum value of 4 at $$\displaystyle{t}={6}$$ hr.

Transformation properties

### If $$\displaystyle{f{{\left(\theta\right)}}}={\tan{\theta}}$$ and $$\displaystyle{f{{\left({a}\right)}}}={2},$$ find the exact value of: a) $$\displaystyle{f{{\left(-{a}\right)}}}$$ b) $$\displaystyle{f{{\left({a}\right)}}}+{f{{\left({a}+\pi\right)}}}+{f{{\left({a}+{2}\pi\right)}}}$$

Transformation properties

### For large value of n, and moderate values of the probabiliy of success p (roughly, $$0.05\ \Leftarrow\ p\ \Leftarrow\ 0.95$$), the binomial distribution can be approximated as a normal distribution with expectation mu = np and standard deviation $$\sigma = \sqrt{np(1\ -\ p)}$$. Explain this approximation making use the Central Limit Theorem.

Transformation properties

### Complete the tasks to determine: a)To graf: The function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}.$$ b)The domain of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}$$ in the interval notation. c)The range of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}$$ in the interval notation. d)The equation of the asymptote of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}.$$

Transformation properties

### Describe how to obtain the graph of g and f if $$g(x)=2(x\ +\ 2)^{2}\ -\ 3,\ h(x)=2x^{2},\ and\ h(x)=2(x\ -\ 3)^{2}\ +\ 2$$

Transformation properties

### To determine the solution of the initial value problem $${y}{''}+{4}{y}= \sin{{t}}+{u}_{\pi}{\left({t}\right)} \sin{{\left({t}-\pi\right)}}:$$ $$y(0) = 0,$$ $$y'(0) = 0.$$ Also, draw the graphs of the solution and of the forcing function and explain the relation between the solution and the forcing function..

Transformation properties

### a) To graph: the $${k}{e}{r}{\left({A}\right)},{\left({k}{e}{r}{A}\right)}^{\bot}{\quad\text{and}\quad}{i}{m}{\left({A}^{T}\right)}$$ b) To find: the relationship between im $$(A^{T})$$ and ker (A). c) To find: the relationship between ker(A) and solution set S d) To find vecx_0 at the intersection of $${k}{e}{r}{\left({A}\right)}{\quad\text{and}\quad}{\left({k}{e}{r}{A}\right)}^{\bot}$$ e) To find: the lengths of $$\vec{{x}}_{{0}}$$ compared to the other vectors in S

Transformation properties