Function: g(x) = (3)-(x+1) + 4 %3D 1. Parent (base) function: 2. List of transformations (with correct vocabulary) that map the base function onto the g(x) function:
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Q: 15. Which of the following is an even function of t? t-sin(t) t'cos(t) sin(t) +t t'sin(t)
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- How do you find the domain for the composition of two functions, fg ?How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)
- Find the domain,range, horizontal asymptote, vertical asymptote and x-intercept of the following Function and show your Solution.please follow my examples for domain and range. Thank you. f(x) = x³ – 1 / x² Domain: Range: Horizontal asymptote: Vertical asymptote: x- Intercept: Example in getting domain and range: f(x) = x / x + 3 Answer: Domain = {x/x≠–3} or (–∞,–3) U (–3,∞) Range = {y/y≠1} or (–∞,1) U (1,∞)Find the domain,range, horizontal asymptote, vertical asymptote and x-intercept of the following Function and show your Solution.please follow my examples for domain and range. Thank you. f(x) = x / x² – x – 6 Domain: Range: Horizontal asymptote: Vertical asymptote: x- Intercept: Example in getting domain and range: f(x) = x / x + 3 Answer: Domain = {x/x≠–3} or (–∞,–3) U (–3,∞) Range = {y/y≠1} or (–∞,1) U (1,∞)Express the rational function that describes the situation.A large mixing tank currently contains 275 gallons of water, into which 5 pounds of sugar have been mixed. A tap will open, pouring 15 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after t minutes.s(t)=
- Sue wants to put a rectangular garden on her property using 80 meters of fencing. There is a river that runs through her property, so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of x.Find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph of the function. f(x)=(x+2)/(x^2−9) Enter the intercepts as points, (a,b). The x-intercept is . The y-intercept is . Vertical asymptotes: x= Horizontal asymptote: y=Apply the properties of functions to correctly determine and interpret the break-even point in the following situations, using valid mathematical procedures and correct mathematical notation. Express your answer in terms of the context of the problem. The total monthly income of a nursery school for caring for x children is given by r = 500x, and its total monthly costs are c = 280x + 2500. How many children need to enroll monthly to break even? In other words, when do revenues equal costs?
- The graph of f(x)=(1.68)xf(x)=(1.68)x is shifted right 33 units, stretched vertically by a factor of 22,,reflected about the xx-axis, and then shifted downward 33 units. What is the equation of the new function, g(x)g(x)? State its yy-intercept (to the nearest thousandth), domain, and range.1) How is the graph of the entire function different from the graph for the real-life situation? 2) Determine increasing interval(s) of the function if it exists. 3) Determine decreasing interval(s) of the function if it exists. 4) As n becomes very large, what happens to C?During the first quarter of the school year the officers –elect of the Supreme Student Government decided to divide their budget evenly to the different committees. If their budget is ₱35,000 construct a function M which would give the amount of money each of the n number of committees would receive.a. You may contruct a table to aid you in determining the relationships between quantities. Number of Committees 2 4 6 8Amount allocated foreach committeeb. Write the rational function that represents the situation