# 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)

Question
Performing transformations
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.

2020-11-23

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 $$f(x) =− 1/4sqrt(16-x^2)-1$$

### Relevant Questions

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
The equation F=−vex(dm/dt) for the thrust on a rocket, can also be applied to an airplane propeller. In fact, there are two contributions to the thrust: one positive and one negative. The positive contribution comes from air pushed backward, away from the propeller (so dm/dt<0), at a speed vex relative to the propeller. The negative contribution comes from this same quantity of air flowing into the front of the propeller (so dm/dt>0) at speed v, equal to the speed of the airplane through the air.
For a Cessna 182 (a single-engine airplane) flying at 130 km/h, 150 kg of air flows through the propeller each second and the propeller develops a net thrust of 1300 N. Determine the speed increase (in km/h) that the propeller imparts to the air.
Determine whether the given set S is a subspace of the vector space V.
A. V=$$P_5$$, and S is the subset of $$P_5$$ consisting of those polynomials satisfying p(1)>p(0).
B. $$V=R_3$$, and S is the set of vectors $$(x_1,x_2,x_3)$$ in V satisfying $$x_1-6x_2+x_3=5$$.
C. $$V=R^n$$, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
D. V=$$C^2(I)$$, and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.
E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.
F. V=$$P_n$$, and S is the subset of $$P_n$$ consisting of those polynomials satisfying p(0)=0.
G. $$V=M_n(R)$$, and S is the subset of all symmetric matrices
For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}$$
A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.
In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?
4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
For the equation (-1,2), $$y= \frac{1}{2}x - 3$$, write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.
consider the product of 3 functions $$\displaystyle{w}={f}\times{g}\times{h}$$. Find an expression for the derivative of the product in terms of the three given functions and their derivatives. (Remeber that the product of three numbers can be thought of as the product of two of them with the third
$$\displaystyle{w}'=$$?
Create a new function in the form $$y = a(x-h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$.