# Recent questions in College algebra

Transformations of functions

### The two linear equations shown below are said to be dependent and consistent: $$2x−5y=3$$ $$6x−15y=9$$ Explain in algebraic and graphical terms what happens when two linear equations are dependent and consistent.

Transformations of functions

### Write an equation in terms of x and y for the function that is described by the given characteristics. A sine curve with a period of $$\pi$$, an amplitude of 3, a right phase shift of $$\pi/2$$, and a vertical translation up 2 units.

Upper level algebra

### The sum of three times a first number and twice a second number is 43. If the second number is subtracted from twice the first number, the result is -4. Find the numbers.

Transformations of functions

### The two linear equations shown below are said to be dependent and consistent: 2x−5y=3 6x−15y=9 What happens if you use a graphical method?

Transformations of functions

### The graph below expresses a radical function that can be written in the form $$f(x) = a(x + k)^{\frac{1}{n}} + c$$. What does the graph tell you about the value of k in this function?

Transformations of functions

### $$\displaystyle{5}{e}^{{0.2}}{x}={7}$$

Transformations of functions

### Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ. $$\displaystyleθ= Transformations of functions ANSWERED asked 2021-06-27 ### Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation. \(\displaystyle\theta={70}^{\circ}$$

Transformations of functions

### Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f (x).$$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -1 & -3 & 4 & 2 & 1 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 \\ \hline g(x) & -1 & -3 & 4 & 2 & 1 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline h(x) & -2 & -4 & 3 & 1 & 0 \\ \hline \end{array}$$

Transformations of functions

### Prove that $$(1+\cos\theta)(1−\cos\theta)=(\sin^2)\theta$$

Transformations of functions

### A back-to-back stemplot is particularly useful for (A) identifying outliers. (B) comparing two data distributions. (C) merging two sets of data. (D) graphing home runs. (E) distinguishing stems from leaves.

Transformations of functions

### find the exact value of $$\tan(\frac{14\pi}{3})$$​​​​​​​ using the unit circle

Transformations of functions

### Write the equation of the circle described. a. Center at the origin, containing the point (-6, -8) b. Center (7, 5), containing the point (3, -2).

Transformations of functions

### An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. To see whether crime mes are related to moon phase, a researcher looks at ten years of archived police blotter reports and compares them with moon charts from the same period.

Transformations of functions

### Simplify $$\displaystyle{x}^{{2}}−{3}{x}−{4}÷{\left({x}+{2}\right)}$$

Upper level algebra

### h is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to h. (c) Sketch the graph of h by hand. (d) Use function notation to write h in terms of the parent function f. $$\displaystyle{h}{\left({x}\right)}={\left({x}−{2}\right)}^{{3}}+{5}$$

Transformations of functions

### Is the vector space $$C \infty[a,b]$$ of infinitely differentiable functions on the interval [a,b], consider the derivate transformation D and the definite integral transformation I defined by $$D(f)(x)=f′(x)D(f)(x)=f′(x)\ and\ I(f)(x)=∫xaf(t)dt f(t)dt$$. (a) Compute $$(DI)(f)=D(I(f))(DI)(f)=D(I(f))$$. (b) Compute $$(ID)(f)=I(D(f))(ID)(f)=I(D(f))$$. (c) Do this transformations commute? That is to say, is it true that $$(DI)(f)=(ID)(f)(DI)(f)=(ID)(f)$$ for all vectors f in the space?

Transformations of functions

### Describe the transformations that must be applied to the parent function to obtain each of the following functions. a) $$\displaystyle{f{{\left({x}\right)}}}=-{3}{\log{{\left({2}{x}\right)}}}$$ b) $$\displaystyle{f{{\left({x}\right)}}}={\log{{\left({x}-{5}\right)}}}+{2}$$ c) $$\displaystyle{f{{\left({x}\right)}}}={\left(\frac{{1}}{{2}}\right)}{\log{{5}}}{x}$$ d) $$\displaystyle{f{{\left({x}\right)}}}={\log{{\left(−{\left(\frac{{1}}{{3}}\right)}{x}\right)}}}−{3}$$

Transformations of functions