Domain - All x values for which a function is defined (input values)Range - Possible y or Output values(-3,-2)EXAMPLE 1DOMAIN AND RANGEgmx)(3,1)a) Find Domain & Range of g(x),The domain is the set of inputs East of the functionInput valves run a long the horizontal axis.21. f(x)=3sin xThe furthest left hout valve associated with a pt. on thegraph is -3. The furthest right input values associatedwith apt, on the graph is 3.So Domain isC-3,3], that is all reals from -3 to 3.The range represents the set of output valves for thefunction. Output valves run a long the vertical axis.The lowest output valve of the function is 2. Thehighest is 1. So the range is [-2, 1], all realsfrem -2to 1.EXAMPLE 2Find the domain and range of f(x)=√√4-x²Write answers in interval notation.DOMAINFor f(x) to be defined 4-x²20.This is true when -2 ≤x≤2Domain: [-2,2]RANGEThe solution to a square root must always bepositive thus f(x) must be greater than or equalto 0.Range: [0,00)Find the domain and range of each function. Write your answer in INTERVAL notation.19. f(x)=x²-520. f(x)=√x+32x-122. f(x)=-

Topic = Functions As per guidelines , At a time only one question can be answered out of different…

Answered: 19. f(x)=x²-5

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 14E

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A triangle is formed by the coordinate axes and a line through the point (2,1), as shown in the figure. The value of y is given by y=1+2x2 Write the area A of the triangle as a function of x. Determine the domain of the function in the context of the problem. Sketch the graph of the area function. Estimate the minimum area of the triangle from the graph.
Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Finding a Minimum Suppose the function f=x392x2+6x+1 describes a physical situation that makes sense only for whole numbers between 1 and 5. For what value of x does f reach a minimum and what is that minimum value?
Learning Curve A learning curve is a graph of a function P(t) that measures the performance of someone learning a skill as a function of the training time t. At first, the rate of learning is rapid. Then, as performance increases and approaches a maximal value M, the rate of learning decreases. It has been found that the function P(t)=MCekt where k and C are positive constants and CM is a reasonable model for learning. a Express the learning time t as a function of the performance level P. b For s pole-vaulter in training, the learning curve is given by P(t)=2014e0.024t where P(t) is the height he is able to pole-vault after t months. After how many months of training is he able to vault 12 ft? c Draw a graph of the learning curve in part b.
Maximum and Minimum Find the maximum and minimum values of f(x)=x39x2+6 on the horizontal span of 0 to 10.
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Concentration of a Mixture A 1000-liter tank contains 50 liters of a 25brine solution. You add xliters of a 75brine solution to the tank. (a) Show that the concentration C, the proportion of brine to total solution, in the final mixture is C=3x+504(x+50). (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch the graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?
Population Growth and Decline The graph shows the population P in a small industrial city from 1950 to 2000. Thevariable x represents the number of year since 1950. (a) Determine the intervals on which the function P isincreasing and on which it is decreasing. (b) What as the maximum population, and in what yearwas it attained? (c) Find the net change in the population P from 1970 to 1990.

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