Concept explainers
Comparing Continuity In Exercises 49 and 50, discuss the continuity of the functions f and g. Explain any differences.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Calculus
- Testing for Functions Represented Algebraically In Exercises 11-18, determine whether the equation represents y as a function of x. x2y=9arrow_forwardFinding Values for Which f(x) = g(x)In Exercises 43–46, find the value(s) of x forwhich f(x) = g(x).43. f(x) = x2, g(x) = x + 244. f(x) = x2 + 2x + 1, g(x) = 5x + 1945. f(x) = x4 − 2x2, g(x) = 2x246. f(x) = √x − 4, g(x) = 2 − xarrow_forwardDetermining Concavity In Exercises 3–14,determine the open intervals on which the graphof the function is concave upward or concavedownward.' 3. f (x) = x2 − 4x + 8arrow_forward
- Applying the continuity theorems For what values of x is the function ƒ1x2= x / x2 - 7x + 12 continuous?arrow_forwardUsing the Vertical Line Test In Exercises 39–42, use theVertical Line Test to determine whether y is a function of x.To print an enlarged copy of the graph, go to MathGraphs.com. 39. x − y2 = 0arrow_forwardThink About It In Exercises 87–92, determine (ifpossible) the zeros of the function g when the function fhas zeros at x = r1, x = r2, and x = r3.87. g(x) = −f(x)88. g(x) = 4f(x)89. g(x) = f(x − 5)90. g(x) = f(2x)91. g(x) = 3 + f(x)92. g(x) = f(−x)Project: Population To work an extended applicationanalyzing the population of the United States, visit thistext’s website at LarsonPrecalculus.com. (Source: U.S.Census Bureau)arrow_forward
- math Prove that f(x) = x ⋅ |x| is continuous at all points c in ℝ.arrow_forwardmathmatics advanced Give an example of an everywhere-defined real function that is continuous at exactly three pointsarrow_forwardEven and Odd FunctionsIn Exercises 47–58, say whether the function is even, odd, or neither. Give reasons for your answer.arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage