Functions f and g are graphed in the same rectangular coordinate system. If g is obtained from f through a sequence of transformations, find an equation for g. (Graph given on the link)

illusiia 2020-11-22 Answered
Functions f and g are graphed in the same rectangular coordinate system. If g is obtained from f through a sequence of transformations, find an equation for g.
(Graph given on the link)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

lobeflepnoumni
Answered 2020-11-23 Author has 25978 answers

Given:
The graph of \(f(x) = sqrt(16−x^2)\)
To determine :
The equation of transformed graph shown in the given figure.
The parent graph of \(f(x) = sqrt(16−x^2)\).
Since the graph is shifted vertically down by 1 unit.
Therefore, the equation becomes,
\(f(x) =sqrt(16-x^2)-1\)
Also, the graph is a reflected graph in the x - axis . Hence we have
\(f(x) =sqrt(16−x^2)− 1\)
Now, the graph is has a vertical compression by 4 units.
Therefore, the transformed graph is \(f(x) =− 1/4sqrt(16-x^2)-1\)
image

Not exactly what you’re looking for?
Ask My Question
39
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-27

Functions f and g are graphed in the same rectangular coordinate system (see attached herewith). If g is obtained from f through a sequence of transformations, find an equation for g
image

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. \(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ \text{and}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)

asked 2021-06-15

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.
\(\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}g({x}{)}=−{\ln{{\left({2}{x}\right)}}}\)

asked 2021-07-30
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.
\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{-{x}}}\)
asked 2021-08-03
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.
\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\)
asked 2021-08-08
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.
\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}\) and \(\displaystyle{g{{\left({x}\right)}}}=-{3}^{{{x}}}\)
asked 2021-02-23
List a sequence of transformations, in words, to convert the graph of \(f(x)=x^2\) into the graph of \(g(x)=-6(x-2)^2+5\).
...