Case(A) Given function is= f(x) = 3-e-xWe have to draw f(x) using transformationof the mother function.Let f(x) = - e-xSo it's graph is given below.-4-3-25-1-2f(x) = -e-x-3If graph of any function y = f(x)is given then graph of the functiony = f(x + a)is the graph obtained by left shifting of thegraph of y = f(x) by the 'a' unit horizontally.So the graph of the function= f(x) = 3-e-xis given below.2f(x) = 3-e-x1-26.-1From the graph, we can see that= Range of the function {f(x) = 3-e*} = (-00,3]

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Answered: Case(A) Given function is = f(x) = 3-ex…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 1DE

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Graph of f(x)= x(x+4)(x-2) Use Graph for part (b) and (c)
Transformations of ƒ(x)= x2 Use shifts and scalings to transform the graph of ƒ1x2= x2 into the graph of g. Use a graphing utility to check your work. a. g1x2= ƒ1x - 32 b. g1x2= ƒ12x - 42 c. g1x2= -3ƒ1x - 22+ 4
Risky Drivers Both inexperienced young drivers andvery old drivers are involved in far more accidents than other age groups. The quartic functionthat models the police-reported crashes for differentage groups is y = 0.00001828x4 - 0.003925x3 +0.3031x2 - 9.907x + 118.2, where x is the age ofthe driver and y equals the number of crashes per million miles traveled.a. Graph the function for the ages 15 to 86.b. What does the model estimate the number ofcrashes per million miles to be for 22-year-olddrivers?c. At what age among older drivers does the modelpredict the number of crashes will reach 8 per million miles?d. At what age among younger drivers does themodel predict the number of crashes will be theminimum number?
Revenue If the price from the sale of x units of aproduct is given by the function p = 100x - x2,the revenue function for this product is given byR = px = (100x - x2)x.a. Find the numbers of units that must be sold to givezero revenue.b. Does the graph of the revenue function verify thissolution?
World Population A low-projection scenario of worldpopulation for the years 1995–2150 by the UnitedNations is given by the function y = -0.36x2 +38.52x + 5822.86, where x is the number of yearsafter 1990 and the world population is measured inmillions of people.a. Graph this function for x = 0 to x = 120.b. What would the world population have been in2010 if the projections made using this model hadbeen accurate?
The graph of a function f is given. The x y-coordinate plane is given. A curve with 2 parts is graphed. The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at x = −1, and ends at the open point (0, −1). The second part is linear, begins at the closed point (0, 2), goes down and right, crosses the x-axis at x = 2, and exits the window in the fourth quadrant. Determine whether f is continuous on its domain. continuous not continuous If it is not continuous on its domain, say why. lim x→0 f(x) ≠ f(0) lim x→0+ f(x) ≠ lim x→0− f(x), so lim x→0 f(x) does not exist. The graph has discontinuities at the end points. The graph is continuous on its domain.
Example 3 Nonlinear functions can lead to some interesting results. Using the functiong(x)= -2|x-2|+4 and the initial value of 1.5 leads to the following result after many iterations. • g(1.5)= -2|1.5-2|+4=2 • g^2 (1.5)=g(3)=2|3-2|+4=2 • g^3 (1.5)=g(2)=-2|2-2|+4=4 • g^4 (1.5) =g(4)=-2|4-2|+4=0 •g^5 (1.5) =g(0)=-2|0-2|+4=0 At this point, further iterations of the function will repeatedly obtain zero. You can conclude that repeated iterations of the function with an initial value of 1.5 will lead to a value of zero. For most values of this function, repeated iterations will lead to looping values. The next set of questions will address this concept. A) What is the loop that forms after many iterations when the initial value of g is 1.7? B) What is the loop that forms after many iterations when the initial value of g is 1.72?
F(x)=x(x-1)(x+1) Graph and show work
How is graph of g(x)=f(kx) related to the graph of f when k=5? The graph of g is a horizontal stretch of the graph of f. The graph of g is a vertical stretch of the graph of f. The graph of g is a horizontal compression of the graph of f. The graph of g is a vertical compression of the graph of f.
draw the graph of f(x+1) draw the graph of f(x)-3 Draw the graph of g(x)=f(-x)
6. The graph of y=j(x) is given. Use transformations to graph the function defined by y=j(-x+1)+3. List the transformations applied to the parent function needed to obtain the graph of y=(-x+1)+3 in the appropriate order. I also need the transformations as well
(a) A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river by? (b) Find the point on the graph of the function that is closest to the given point: f(x) = 3x; (0,2)

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