 Recent questions in College algebra
Transformations of functions
ANSWERED ### Describe how the given functions can be obtained from their basic (or parent) function f using transformations. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}},{g{{\left({x}\right)}}}=\sqrt{{{2}{x}-{10}}}$$

Transformations of functions
ANSWERED ### The function g is related to one of the parent functions described in an earlier section. $$\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{6}}}}\sqrt{{{x}}}$$ a) Identify the parent function f. b)Describe the sequence of transformations from f to g. c)Use function notation to write g in terms of f. g(x)=(?)f(x)

Transformations of functions
ANSWERED ### What transformations of the parent graph of $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{c}}$$ produce the graphs of the following functions? a) $$\displaystyle{m}{\left({x}\right)}=\sqrt{{{7}{x}-{3.5}}}-{10}$$ b) $$\displaystyle{j}{\left({x}\right)}=-{2}\sqrt{{{12}{x}}}+{4}$$

Transformations of functions
ANSWERED ### Begin by graphing $$\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}$$ Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. $$\displaystyle{g{{\left({x}\right)}}}={{\log}_{{{2}}}{\left({x}-{2}\right)}}$$

Transformations of functions
ANSWERED ### Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}+\sqrt{{{x}}}$$

Transformations of functions
ANSWERED ### Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes Use the graphs to determine each function's domain and range. $$\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}$$

Transformations of functions
ANSWERED ### Begin by graphing $$\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}$$. Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. $$\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}$$

Transformations of functions
ANSWERED ### Describe the transformations and sketch the graphs of the following trigonometric functions. $$\displaystyle{a}.{f{{\left({x}\right)}}}=-{2}{\cos{{\left({2}{x}\right)}}}+{3}\\ {b}.{g{{\left({x}\right)}}}={3}{\sin{{\left({x}-\pi\right)}}}-{1}$$

Transformations of functions
ANSWERED ### Begin by graphing $$f(x)= \log_{2}x.$$ Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each functions domain and range. $$\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}$$

Transformations of functions
ANSWERED ### Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. $$\displaystyle{f{{\left({x}\right)}}}={\log{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}=-{\log{{\left({x}+{3}\right)}}}$$

Transformations of functions
ANSWERED ### Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain arid range. $$\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}$$

Transformations of functions
ANSWERED ### Begin by graphing $$\displaystyle{f{{\left({x}\right)}}}={\log{{2}}}{x}$$ Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each functions domain and range. $$\displaystyle{r}{\left({x}\right)}={{\log}_{{{2}}}{\left(-{x}\right)}}$$

Transformations of functions
ANSWERED ### Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. $$\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{-{x}}}$$

Transformations of functions
ANSWERED ### For $$\displaystyle{y}={3}+{{\log}_{{{2}}}{x}}$$. a) Use transformations of the graphs of $$\displaystyle{y}={{\log}_{{{2}}}{x}}$$ and $$\displaystyle{y}={{\log}_{{{3}}}{x}}$$ o graph the given functions. b) Write the domain and range in interval notation. c) Write an equation of the asymptote.

Transformations of functions
ANSWERED ### 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
ANSWERED ### 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 $$\frac{\pi}{2}$$, and a vertical translation up 2 units.

Upper level algebra
ANSWERED ### 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
ANSWERED ### 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
ANSWERED ### 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?
ANSWERED 