7. (8 pts) A graph ofy-f(a) follows. No formula for fis given. Which graph (A, B,...
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of the function and sketch a graph of its derivative directly beneath. a) b) c) 0 any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x-3)2 at P-(1,...
Problem 2. (12 pts) The graph of a function fis given below. Answer the questions that follow. 110 6 2- 5 -6- - X-2 (i) (6 pts) Find the following limits. If a limit is infinite or does not exist, specify so. (Ipt each) a) lim f(x) = b) lim f(x)= c) limf(x) = d) lim f(x) = e) lim f(x) = g) limf(x) = (2 pts) Does f have any asymptote(s)? If yes, what kind? Write their equations. (iii)...
Problem 7. (10 pts) The graph of f'(x) is given below. If f(0) = 5, find f(x) at I = 2, 2 = 6, and I=10. y f'(x) 3 4 2 5 10 -1 2
9. (5 pts) A graph of f(x) is below. No formula is given. On the second set of axes, draw the graph of the function g(x) = f(x+2)-1. foxy 3 2 -1 1 12 2 3 4 56 1 2 3 56 -6-5 -4 -3 -2 -1 0 -1 -6 -5 4 3 2 -1 0 -1 -2 2 O -3 -30 4 -4 -5 -6 -5 -6
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
both if you can. with each step
Suppose the graph of fis given. Describe how to obtain the graph of y=-2/(x-4) starting from the graph of y = f(x) and using a sequence of transformations. 16) Verify that the graph of the equation 3x+2xy = 1 is symmetric with respect to the x axis by using the correct test for symmetry. Using the graph in any way will not count towards justifying your answer.
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
The function f(x) is given by the graph below: (a) Write a piece-wise formula for f(x): (b) Determine if each of the following graphs are simple (single shifts, scalings, or reflections) transformations of f(x). If it is, write a formula for the graph in terms of f. Otherwise, explain why it is not
The function f(x) is given by the graph below: (a) Write a piece-wise formula for f(x): (b) Determine if each of the following graphs are simple (single...
6. (10 points) The graph of a function fis given below. 2 a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity (jump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: i. lim f(x) ii. limf(x) ill. lim f(x) 22+
6. (10 points) The graph of a function fis given below. O O a. For which values of x in the interval (-4,4) is fnot continuous? Give the type of discontinuity (jump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: i. lim f(x) lll. lim f(x) X-2 X-2 X-2