Transformations of functions, solved and explained

Recent questions in Transformations of functions

Transformations of functions

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asked 2021-10-06

If \(f(x) = x + 4\) and \(\displaystyle{g{{\left({x}\right)}}}={4}{x}²\), find \((f + g)(x)\) and \((f + g)(2)\).

Transformations of functions

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asked 2021-09-30

Given that f(x) = 3x - 7 and that (f + g)(x) = 7x + 3, find g(x).

Transformations of functions

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asked 2021-09-30

g is related to one of the parent functions. Describe the sequence of transformations from f to g.

\(g(x) = 2 - (x + 5)^2\)

Transformations of functions

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asked 2021-09-29

use long division to determine if 2x-1 is a factor of \(\displaystyle{p}{\left({x}\right)}={6}{x}^{{3}}+{7}{x}^{{2}}-{x}-{2}\)

Transformations of functions

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asked 2021-09-29

\(\displaystyle{f{{\left({x}\right)}}}={9},{\quad\text{if}\quad}{x}\le-{4},{\quad\text{and}\quad}{f{{\left({x}\right)}}}={a}{x}+{b},{\quad\text{if}\quad}-{4}{<}{x}{<}{5},{\quad\text{and}\quad}{f{{\left({x}\right)}}}=-{9},{\quad\text{if}\quad}{x}\ge{5},\)
Find the constants, if the function is continuous on the entire line.

Transformations of functions

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asked 2021-09-28

Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}{g}⟨{x}{)}=−{\ln{{\left({2}{x}\right)}}}\)

Transformations of functions

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asked 2021-09-27

x=-8, when \(\displaystyle{y}=-\frac{{1}}{{4}}\) in an inverse variation.
Find y, when x=4.

Transformations of functions

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asked 2021-09-26

Describe the transformations that were applied to \(\displaystyle{y}={x}^{{{2}}}\) to obtain each of the following functions. \(\displaystyle{a}{)}{y}=-{2}{\left({x}-{1}\right)}^{{{2}}}+{23}\ {b}{)}{y}={\left({\frac{{{12}}}{{{13}}}}{\left({x}+{9}\right)}\right)}^{{{2}}}-{14}\ {c}{)}{y}={x}^{{{2}}}-{8}{x}+{16}\ {d}{)}{y}={\left({x}+{\frac{{{3}}}{{{7}}}}\right)}{\left({x}+{\frac{{{3}}}{{{7}}}}\right)}\ {e}{)}{y}={40}{\left(-{7}{\left({x}-{10}\right)}\right)}^{{{2}}}+{9}\)

Transformations of functions

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asked 2021-09-24

Show that f is inverse of g and vice-versa, if
f(x)=x-6 and g(x)=x+6

Transformations of functions

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asked 2021-09-24

Given:
\(\displaystyle\frac{m}{{8}}=\frac{15}{{24}}\)
Is \(\displaystyle{8}\times{m}={25}\times{15}\) true or false? Correct if false. Find m.

Transformations of functions

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asked 2021-09-23

Find domain of fog, if
1. \(\displaystyle{f{{\left({x}\right)}}}={x}+{5};{g{{\left({x}\right)}}}=\frac{{7}}{{{x}+{7}}}\)
2. \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{x}};{g{{\left({x}\right)}}}={6}{x}+{18}\)

Transformations of functions

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asked 2021-09-22

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. h(x)=√x−1+4

Transformations of functions

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asked 2021-09-21

\(\displaystyle{f}:{R}\to{R}\)
f(x)=7x-3
Prove that f is onto.

Transformations of functions

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asked 2021-09-21

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f. \(\displaystyle{g{{\left({x}\right)}}}=−{\left({x}+{3}\right)}^{{3}}−{10}\)

Transformations of functions

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asked 2021-09-20

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

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asked 2021-09-19

Sketch a graph of the function. Use transformations of functions whenever possible.
\(f(x)=\begin{cases}1-x & if & x<0 \\1 & if & x\geq0\end{cases}\)

Transformations of functions

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asked 2021-09-17

g(x)
\(\displaystyle=\frac{{{2}{x}^{{2}}-{3}{x}-{20}}}{{{x}-{4}}},{\quad\text{if}\quad}{x}\ne{4}\)
and
=kx-15, if x=4
Evaluate the constant k that makes the function continuous.

Transformations of functions

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asked 2021-09-17

Given:
n=3;
4 and 2i are zeros;
f(-1)=75
Find an nth-degree polynomial function with real coefficients

Transformations of functions

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asked 2021-09-17

Given an indicated variable:
S=180n-360
Solve it for n

Transformations of functions

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asked 2021-09-17

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. \(\displaystyle{g{{\left({x}\right)}}}=√\frac{{1}}{{4}}{x}\)

Regardless if you are dealing with transformations of exponential functions or want to solve quadratic function equations, we have all the right answers for you that are based on the most common questions. These answers below are meant to help you find the starting points as you are dealing with this part of Algebra for your college task.

Have no worries if you cannot find your question below because mathematical transformations of exponential functions are mostly the same, which is why understand at least one example correctly will be of help.

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Transformation of functions questions and answers