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SECONDARY
CALCULUS AND ANALYSIS
PRECALCULUS
TRANSFORMATIONS OF FUNCTIONS
Secondary
Calculus and Analysis
Precalculus
Matrices
Polynomials
Probability and combinatorics
Composite functions
Vectors
Trigonometry
Complex numbers
Series
Polynomial graphs
Transformations of functions
Calculus 1
Calculus 2
Algebra
Geometry
Statistics and Probability
Math Word Problem
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Transformations of functions Answers
Transformations of functions
asked 2021-03-18
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}=-{\left({x}-{1}\right)}^{{{4}}}\)
Transformations of functions
asked 2021-03-12
Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions.
\(\displaystyle{y}={\ln{{\left({2}-{x}\right)}}}\)
Transformations of functions
asked 2021-02-21
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
\(\displaystyle{R}{n}{\left({x}\right)}\rightarrow{0}\)
.]
\(\displaystyle f{{\left({x}\right)}}={e}-{5}{x}\)
Transformations of functions
asked 2021-02-14
Begin by graphing
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}.\)
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
\(\displaystyle{g{{\left({x}\right)}}}={2}^{{{x}}}={2}^{{{x}}}\ +\ {2}\)
Transformations of functions
asked 2021-02-12
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}={1}-\sqrt{{{x}}}+{2}\)
Transformations of functions
asked 2021-02-10
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.
\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}={3}^{{{x}}}\ -\ {1}\)
Transformations of functions
asked 2021-02-08
Begin by graphing
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\)
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
\(\displaystyle{g{{\left({x}\right)}}}=-{2}^{{{x}}}\)
Transformations of functions
asked 2021-01-31
Use long division to rewrite the equation for g in the form
\(\displaystyle\text{quotient}+{\frac{{{r}{e}{m}{a}\in{d}{e}{r}}}{{\div{i}{s}{\quad\text{or}\quad}}}}\)
Then use this form of the function's equation and transformations of
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
to graph g.
\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}\)
Transformations of functions
asked 2021-01-22
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1}\)
Transformations of functions
asked 2021-01-16
Sketch a graph of the function. Use transformations of functions when ever possible.
\(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{3}}}{\left\lbrace-{x}\right\rbrace}\)
Transformations of functions
asked 2021-01-10
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 vertical asymptote? Use the graphs to determine each function s domain and range.
\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}{{\log}_{{{2}}}{x}}\)
Transformations of functions
asked 2021-01-10
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 vertical asymptote? Use the graphs to determine each function's domain and range.
\(\displaystyle{g{{\left({x}\right)}}}=\ -{2}\ {{\log}_{{{2}}}{x}}\)
Transformations of functions
asked 2020-12-24
Begin by graphing
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}.\)
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
\(\displaystyle{g{{\left({x}\right)}}}={2}^{{{x}\ +\ {2}}}\)
Transformations of functions
asked 2020-12-22
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}={\left|{x}\ +\ {1}\right|}\)
Transformations of functions
asked 2020-12-15
In the following items, you will analyze how several transformations affect the graph of the function
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
. Investigate the graphs of
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}},{g{{\left({x}\right)}}}={f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}+{2}}}},{h}{\left({x}\right)}={\frac{{{1}}}{{{x}-{2}}}},{p}{\left({x}\right)}={\frac{{{1}}}{{{x}-{4}}}}\ \text{and}\ {z}{\left({x}\right)}={\frac{{{1}}}{{{x}^{{{2}}}+{1}}}}\)
. If you use a graphing calculator, select a viewing window
\(\displaystyle\pm{23.5}\)
for x and
\(\displaystyle\pm{15.5}\)
for y. At what values in the domain did vertical asymptotes occur for each of the functions? Explain why the vertical asymptotes occur at these values.
Transformations of functions
asked 2020-12-15
Standard transformations can be used to help graph rational functions of the form
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{A}}}{{{B}{x}-{C}}}}+{D}\)
Explain how the parameters A, B, C, and D relate to the graph of the rational functions.
Transformations of functions
asked 2020-11-23
Graph f and g in the same rectangular coordinate system. Use transformations of the graph f of to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\text{and}{g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)
Transformations of functions
asked 2020-11-12
Let
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={x}\ -\ {3}.\)
a) Determine the equations of the composite functions
\(\displaystyle{\left({f}\ \circ\ {g}\right)}{\left({x}\right)}\ {\quad\text{and}\quad}\ {\left({g}\ \circ\ {f}\right)}{\left({x}\right)}.\)
b) Graph the composite functions. c) Graph the composite functions. Describe
\(\displaystyle{\left({f}\ \circ\ {g}\right)}{\left({x}\right)}\ {\quad\text{and}\quad}\ {\left({g}\ \circ\ {f}\right)}{\left({x}\right)}\)
as transformations of f(x).
Transformations of functions
asked 2020-11-12
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 vertical asymptote? Use the graphs to determine each function's domain and range.
\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}\ {{\log}_{{{2}}}{x}}\)
Transformations of functions
asked 2020-11-09
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {1}\right)}^{{{3}}}}}}\)
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