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19. f(x) X x² - 4 x²

19. f(x) X x² - 4 x²

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.CT: Chapter Test
Problem 4CT: Find f(1) and f(2). f(x)=x+7
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, sketch a graph of the given function using Key Idea 3.5.1 Show all work; check your answer with
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19. f(x) = x² - 4 x²
Transcribed Image Text:19. f(x) = x² - 4 x²
Key Idea 3.5.1 Curve Sketching To produce an accurate sketch a given function f, consider the following steps. 1. Find the domain of f. Generally, we assume that the domain is the entire real line then find restrictions, such as where a denominator is 0 or where negatives appear under the radical. 2. Find the critical values of f. 3. Find the possible points of inflection of f. 4. Find the location of any vertical asymptotes of f (usually done in conjunction with item 1 above). 5. Consider the limits lim f(x) and lim f(x) to determine the end *4-x x+x0 behavior of the function. 6. Create a number line that includes all critical points, possible points of inflection, and locations of vertical asymptotes. For each interval created, determine whether fis increasing or decreasing, concave up or down. 7. Evaluate f at each critical point and possible point of inflection. Plot these points on a set of axes. Connect these points with curves exhibiting the proper concavity. Sketch asymptotes and x and y intercepts where applicable.
Transcribed Image Text:Key Idea 3.5.1 Curve Sketching To produce an accurate sketch a given function f, consider the following steps. 1. Find the domain of f. Generally, we assume that the domain is the entire real line then find restrictions, such as where a denominator is 0 or where negatives appear under the radical. 2. Find the critical values of f. 3. Find the possible points of inflection of f. 4. Find the location of any vertical asymptotes of f (usually done in conjunction with item 1 above). 5. Consider the limits lim f(x) and lim f(x) to determine the end *4-x x+x0 behavior of the function. 6. Create a number line that includes all critical points, possible points of inflection, and locations of vertical asymptotes. For each interval created, determine whether fis increasing or decreasing, concave up or down. 7. Evaluate f at each critical point and possible point of inflection. Plot these points on a set of axes. Connect these points with curves exhibiting the proper concavity. Sketch asymptotes and x and y intercepts where applicable.
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