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 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 3Sketch 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.
- 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.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 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).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