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- 1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0Let ƒ(x) = (3^x - 1)/x. a. Make tables of values of ƒ at values of x that approach c = 0 from above and below. Does ƒ appear to have a limit as x --> 0? If so, what is it? If not, why not? b. Support your conclusions in part (a) by graphing ƒ near c = 0.1)Sketch the graph of a function with the following properties: f(x) has the following points : (-2,4) (0,2) (2,1) and (3,0)f(x) increasing : nowhere f(x) concave up : (−2,0) ∪ (2,3)f(x) decreasing : (−∞, ∞) f(x) concave down : (−∞, −2) ∪ (0,2) ∪ (3, ∞)f(x) has a horizontal asymptote at Y= 5 and a vertical asymptote at x= 4
- 4(2) Show, and explain well your calculations. Please find: A) Image of the function given. B) Intervals where the g(x) function is positive or negative. C) Growth and decay intervals of the g(x) function. D) The intersection points of the affine function and its inverse.F(x)=x(x-1)(x+1) Graph and show workLet G(x) = (x + 6)/(x2 + 4x - 12). a. Make a table of the values of G at x = -5.9, -5.99, -5.999, and so on. Then estimate limx--> -6 G(x). What estimate do you arrive at if you evaluate G at x = -6.1, -6.01, -6.001, .....instead? b. Support your conclusions in part (a) by graphing G and using Zoom and Trace to estimate y-values on the graph as x --> -6
- Movie expenditures, in billions of dollars, on advertising in a certain format from 1995 to 2004 can be approximated by f(t) = 0.04t + 0.33 if t ≤ 4 −0.01t + 1.5 if t > 4, where t is time in years since 1995. (a) Compute lim t→4− f(t). (If an answer does not exist, enter DNE.) Interpret the answer. Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion. Compute lim t→4+ f(t). (If an answer does not exist, enter DNE.) Interpret the answer. Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion. (b) Is the function f continuous at t = 4? YesNo What does the answer tell you about movie advertising expenditures? Movie advertising expenditures in 1999.Below is a graph of the function g(x). Use this graph to complete the problems given below. a) lim x->2 g(x) =? b) lim x->0 g(x) =? c) lim x->4- g(x) =? d) lim x->4+ g(x) =? Based on the answrs in c and d does lim x->4 g(x) exist?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)
- 5. Given the graph of g(x) = {√−x−2+1, x<-2 x2+2x+5, x≥-2 below, evaluate its limit as x approaches -2. a. 3 b. 1 c. the limit does not exist d. 5 6. Evaluate lim g(x) x→-3-. a. 18 b. - ∞ c.0 d. ∞ 7. Let g(x) = -1/x2. Evaluate lim g(x) x→0 by drawing its graph. a. ∞ b. 1 c. 0 d. -∞a)Find the domain of the function f and graph the domain of f. b) Show that lim (x,y) —>(0,1) f (x, y) cannot be found.Suppose that the function y = f(x) is increasing on the interval [- 1, 5].(a) Over what interval is the graph of y = f(x + 2) increasing?(b) Over what interval is the graph of y = f(x - 5) increasing?(c) What can be said about the graph of y = - f(x)?(d) What can be said about the graph of y = f( - x)?