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13-15 Sketch the graph of a function that satisfies the given conditions.
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- a) Sketch the graph of the function f (x) = {2x – 3 if x 2 %3D then evaluate lim f(x), lim f(x) at a = 2. X --> a+ X --> a- b) Find the derivative of the following function f (x) = 3x5 – 2x4 + 3x2 - 2x + 1 %3D c) Find the derivative of the following function g (x) = (1+x) e d) Find the derivative of the following function h (x) = (x + ) %3Darrow_forwardB The graph of a function f with f (b) > f (a) is shown above for a ≤ x ≤ b. The derivative of f exists for all x in the interval a < x < b except x = 0. For how many values of c, for a < c < b, does lim f(x)-f(c) f(b)-f(a) x-c b-a X-C Zero Two Three (a, f(a)) Four = (b, f(b)) ? Varrow_forward2x+3 - X 1. Sketch a graph of f(x) = { 3 1-x² if x -1 if x 2 2. Sketch a graph of h(x) = { X 3. Consider the graph of y = f(x) below: -3 y YA 2 0 (a) Let S = (-1,2] be a subdomain for the graph above. What is I (b) Let U = (-1,3] be a subdomain for the graph above. What is I (c) Write a piecewise function for the graph. 4. Consider the graph of y = h(x) below: 3 0 h 3 X (a) Find the values of h(-2), h(0), h(2), and h(3). (b) Determine the (usable) domain and range of h. (c) Find the values of x for which h(x) = 3. (See next page.) Xarrow_forward
- 1Qarrow_forwardExample 2: Shift the graph of the function fx) = x; if DF{x: -2arrow_forward3 2 1 1 3 5 Graph of f 34. The graph of the function ƒ is shown above. Which of the following statements are true? I. lim→0 f(2.25+h)-f(2.25) = f'(5). II. 6-13) = . 5-3 2 III. f"(1) < f"(5). (a) I only (b) II only (c) III only (d) I and III only (e) None are true.arrow_forward1. Consider the graph of the function f (x). (a) Find all the points where f(x)is discontinuous. (b) What kind of discontinuityis each point?arrow_forwardUse the given graph of f(x) = x² to find a number 8 such that if |x-1|< 8 then x²-1| (Round your answer down to three decimal places.) 8 = y 1.5 1- 0.5 0 ? ? y=x² xarrow_forwardarrow_back_iosarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage