Concept explainers
In Exercises 79-82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.)
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University Calculus
- In Exercises 1-3, find the domain of the function and identify any asymptotes of the graph of the function. f(x)=3x23+x2arrow_forwardSketch the graph of an example of a function f that satisfies all of the given conditions. lim x→0 (f(x)) = ∞, lim x→3− (f(x)) = −∞, lim x→3+ (f(x)) = ∞, lim x→−∞ (f(x)) = 3, lim x→∞ (f(x)) = −2arrow_forwardThe graph of a function f for which f(2) exists and lim f(x) x-->2 exists, but the two are not equal. Construct an example of thisarrow_forward
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- The greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is the unique integer such that n < x < n + 1.Sketch the graph of y = [ x ] . Calculate for c an integer:(a) lim [ x ] (b) lim [ x ] ( c) lim [ x ] x→ c x→ c+ x→ 2.6arrow_forwardSketch the graph of a function y = f(x) with all of the following properties: a) f ′(x) > 0 for −2 ≤ x < 1 b) f ′(2) = 0 c) f ′(x) > 0 for x > 2 d) f(2) = 2 and f(0) = 1 e) lim x → −∞ f(x) = 0 and lim x → ∞ f(x) = ∞ f) f ′(1) does not existsarrow_forwardUse Calculus to find the absolute maximum and the absolute minimum of the function over the indicated interval. f(x)= x^3+x^2-x+1 ; [-2, 1/2]arrow_forward