8. Sketch the graph of the function with por and vertical asymptote at x=1 and horizontal asymptote at y = 1. Label the extrema and points of inflection. f(x) -2 0 1 2 + f''(x) 2 0 2 3
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- Let P = (x, y) be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point (0, - 1) as a function of x.(b) What is d if x = 0?(c) What is d if x = - 1?(d) Use a graphing utility to graph d = d(x).(e) For what values of x is d smallest?Sketch the graph of the given function. Check your sketch using technology. f(x)=x^2+4x+4 (a) indicate the X and Y intercepts. (b) indicate any extrema (x,y) (c) indicate any points of inflection. (d) indicate the behavior near singular points of F. (e) indicate the behavior at infinity. 2.Consider the function f ( x)=5 x^2−3 x+1 / x^2−5 x−14 a) State the domain of f(x) using interval notation.b) Find the equation of the horizontal asymptote(s) (if any).c) Find the equation of the vertical asymptote(s) (if any).
- The graph of the function f(x) is shown below. It consists of a semicircle and two straight line segments. 50 -3 -2 y 3 2 -1 1 2 (a) Which of the following numbers is the largest: f'(-3.95), ƒ' (-1.5), ƒ' (-0.05), ƒ' (1), ƒ' (3.05)? 3 4 5 XUse the graph of f and g. p(x) = f(x)g(x) f(x) g(x) q(x) y 10 8. f 4 2 -2 4 6. 8 10 -2 (a) Find p'(2). p'(2) = (b) Find q'(4). q'(4) = 2.Sketch the graph of the function with points (-2,0), (0,0) and (2,0) (4,2) and vertical asymptote at x = 1 and horizontal asymptote at y = 1. Label the extrema and points of inflection. f'(x) -2 0 1 2 f'(x) + 2 0 + 2 3
- 2 Find all points (x,y) on the graph of f(x) = 3x² - 4x with tangent lines parallel to the line y=8x+5. The point(s) is/are (TV noir ad)1.) sketch the graph f(x)=2^-x -3. stte vertical shift, horizontal shift, ordered pair where (0,1) transforms to, eqaution of asymptote.Consider the function h(x) = 1/5 x^5 − 1/3 x^3 + 2. a) Using derivatives, find the interval(s) where ℎ is increasing and the interval(s) where h is decreasing. b) Using the second derivative test, determine the location of each local maximum or minimum. c) Sketch the graph of y = h(x) using the data you gathered in parts a) and b).
- The diagram shows the graph of y = f(x) which is made up of line segments and a parabola. y 4 2 -5 -4 -3 -2 -1 1 3 4 -1 -2 -3 -4 -5 (a) State the values of x for which f'(x) does not exist. (b) Sketch the graph of y = f'(x) on the same diagram above.Consider the graph of y = f(x). 3+ + -3 -2 (a) f'(-4)= (b) f'(4) = - 1 -1 -2 -3+ LA (c) Determine all x where f'(x) is undefined. x = Write your answer(s) from lowest to highest, separated by commas. (d) Determine all x where f'(x) = 0. x= Write your answer(s) from lowest to highest, separated by commas.Use a graph to estimate all the vertical and horizontal asymptotes of the curve y=7- 2x + 1 x' - 2x + 1