Concept explainers
Sketching graphs Sketch a possible graph of a function f that satisfies all the given conditions. Be sure to identify all vertical and horizontal asymptotes.
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Calculus: Early Transcendentals (2nd Edition)
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- Determine the asymptotes of the function based on the information in the picture. Label if vertical, horizontal or oblique asymptote.arrow_forwardTutorial Exercise Use the given graph of the function y = f(x) to find the following quantities, if they exist. y 3 1 -6 -5 -4 -3 -2 -1 1 (a) lim f(x) X-4 (b) lim f(x) X-1- (c) x--1+ lim f(x) (d) lim f(x) x--1 (e) f(-1) Step 1 of 3 (a) lim f(x) X→-4 Recall lim f(x) exists if and only if lim f(x) = lim f(x). a+ Xa Xa Also recall lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a for Xa x a. Using the graph, find the values (if they exist) of lim f(x) and lim f(x). (If a limit does not exist, enter DNE.) X→-4+ X-4- lim f(x) = X→-4- lim f(x) = X→-4+ O, lim f(x) ---Select--- X--4 O and its value is as follows. (If the limit does not Since these limits -Select--- exist, enter DNE.) lim f(x) = X-4arrow_forwardInstructions as number 1: Please sketch the graph of f and evaluate each. Use appropriate superscripts.arrow_forward
- A function fis given. f(x) = 7 - 2x, 1arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) -4. 2 4 lim f(x) x-2 (a) lim f(x) (b) x- 2* (c) lim f(x) x- 2 (d) f(2) (e) lim f(x) x-4 (f) (4)arrow_forwardB. LIMITS at INFINITY Recall your lesson in Piece-wise function. X→C In this lesson, you must be able to differentiate between f(c) and lim f(x). In evaluating a function f(c), when you do DIRECT SUBSTITUTION, the result must be a DEFINED NUMBER (A NUMBER THAT EXIST), otherwise f(c) is UNDFINED. Contrary to lim f(x), when you do direct substitution, the answer maybe indeterminate 0/0 but THERE IS A WAY TO EVALUATE THE LIMIT USING MANY TECHNIQUES, otherwise lim f(x) DOES NOT EXIST. x→c X-C Let us examine the piece-wise function below. 0 1. f(-4) 2. f(-2) 3. f (0) The function is defined by the equation. 4. f (1) 5. f(2) 6. f (3) f(x) = 2+7, -4≤x≤-2 -2, 7. f (4) 8. f(7). -1, (x-2)², x-4 x-7 7 A Self-Regulated Learning Module 2arrow_forwardActivity x? -1 a. Find lim f(x) if f(x)= x+1 x-1 b. Complete the table of values. -2 -1.5 -1.1 -1.001 -1 -0.9 -0,5 -0,1 x -1 f(x)= x+1 lim f(x) I-1arrow_forwardSketch the graph of a function f with domain R that satisfies all conditions below simultaneously. For this question only, you do not need to prove or explain your answer, as long as the graph is correct and very clear. We want only one single function f that satisfies all the conditions, all at once. Make your graph tidy and unambiguous. 1. lim f(x) = 2 7. lim f(x) = 5 I-1 2. lim f(x) exists for every a e R, 8. lim [f(x)]? = 1 except a = -2 ,a = 2 and a = n. 9. lim f(f(x)) = 3 3. lim f(x) = f(2) I+2+ 10. lim f(x) = -1 4. lim f(f(x)) = 5 11. lim f(2/(x) – 1) = 0 5. |f(r)| # 1 I-2 6. lim f(x) # f(3) 12. lim f(f(x)) = -3 I-3 I-1arrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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