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- 4. Find the equation for a polynomial function in factored form with zeroes at x=-1 order 3 and at x=1 order 2 and the graph passes through (-2, 18). (5)1. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 - 4 / x - 2 are the same in every respect. Provide evidence to support your position. 2. Do you agree with the statement that “ cubic functions must have at least 1x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts.Provide evidence to support your position.Consider the general equation of a quadratic function: f(x)=ax2+bx+cf(x)=ax2+bx+c (Recall: aa, bb, and cc represent constants). Use the derivative f′(x)f′(x) to find the critical value of f(x)f(x) in terms of aa and bb (does this formula look familiar?) Use the second-derivative test to show that the critical value is a local maximum if a<0a<0 or a local minimum if a>0a>0. What determines whether the graph of f(x)f(x) is concave up or concave down? Does the graph of f(x)f(x) have any inflection points? Explain.
- the cubic polynomial shown below has zeros at x= -4 and x=2 only has a relative maximum at (-2,8). which of the following is its y-value when x=6???????? ? (a) (i) Lim 5x −3 − 4/ 2x −2 + 9 x→∞ (ii) Lim (x − 3) 2/x2/2 − 2x − 3 x→∞ During a nationwide program to immunize the population against a new strain of the flu, public health officials determined that the cost of inoculating x% of the susceptible population would be approximately C(x) = 1.85x/100 - x million dollars. (i) What would it cost to providing immunization to the first 20% of the susceptible population? (ii) What would it cost to providing immunization to the next 30% of the susceptible population? (iii) Suppose 17 million dollars are available for providing immunization. What percentage of the susceptible population will not receive immunization? (iv) If money was not a problem will they be able to providing immunization to the entire susceptible population? (c) Determine the values of x for which the function f(x) = {2x2 – 4 x < 2 {x + 2 2 < x > 5 {7 x ≥ 5 is…In Problems 17–22, form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary dependingon the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.
- 1. Factor f(x) into linear factors. Use synthetic division. a.) f(x)= x³ + x² - 5x - 5 b.) f(x)= 3x⁴ - 11x³ + 15x² - 9x + 2 2. Suppose that the quantity supplied S and the quantity demanded D of sandwich at a baseball game are given by the following functions. S(p)= -1000 + 5000p D(p)= 10000 - 2500p Where p is the price of a sandwich. a. Find the equilibrium price for sandwiche at a baseball game. What is the equilibrium quantity? b. Determine the price for which quantity demanded is less than quantity supplied.Find a cubic polynomial f(x)=ax^3+bx^2+cx+d that has horizontal tangents at the points (-3,2) and (2,-4). The answer y=0.096x^3+0.144x^2-1.728x+1.888 is incorrect. The answer y=1/15x3+1/10x2-6/5x-10 is also incorrect.year 2000 2005 2010 2015 2016 2020 2024 enrollement 47,794 49549 50354 50959 5122 52114 53938 A). use cubic regression to find a third-order polynomial function9(x) that models this data g(x)=( )x3+( )x2+ ( )x+( )
- A quadratic function f(x) has its vertex at the point (1, −4) and one of its x-intercepts is (3, 0)8-The rational function y=ax2/(bx2+(2b+1) x +b) has one verticalasymptote and passes through point (2, -3) determine the values of aand b.In Problem,form a polynomial function f(x) with real coefficients having the given degree and zeros.Answers will vary depending on the choice of the leading coefficient.