DISCOVER: Graph of the Absolute Value of a Function(b) Draw graphs of the functions f(x) = x – 6x² andg(x) = |x* – 6x² |. How are the graphs of f and g(a) Draw graphs of the functionsf(x) = x? + x- 6related?(c) In general, if g(x) = |f(x)|, how are the graphs of fand g related? Draw graphs to illustrate your answer.andg(x) = |x² + x - 6|How are the graphs of f and g related?

The function g(x) is the modulus function of the function f(x). Graph of both the functions can be…

Answered: DISCOVER: Graph of the Absolute Value…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter5: Polynomial And Rational Functions

Section5.5: Zeros Of Polynomial Functions

Problem 49SE: Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph...

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Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 49. f(x)=x32x2+x1
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Given; f(x) = x3 - x2 - 9x + 9 , Solve; a. Use the Leading Coefficient Test to determine the graph’s end behavior. b. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. c. Graph the function.
Revenue If the price from the sale of x units of aproduct is given by the function p = 100x - x2,the revenue function for this product is given byR = px = (100x - x2)x.a. Find the numbers of units that must be sold to givezero revenue.b. Does the graph of the revenue function verify thissolution?
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How to Graph a Quadratic Function by HandUsing Its PropertiesGraph f1x2 = - 3x2 + 6x + 1 using its properties. Determine the domain and therange of f. Determine where f is increasing and where it is decreasing. EXAMPLE 3 Step-by-Step SolutionStep 1: Determine whether thegraph of f opens up or down.Step 2: Determine the vertex andaxis of symmetry of the graph of f.Step 3: Determine the intercepts ofthe graph of f. In Example 2, it was determined that the graph of f1x2 = - 3x2 + 6x + 1 opensdown because a = - 3 6 0.In Example 2, the vertex was found to be at the point whose coordinates are (1, 4).The axis of symmetry is the line x = 1.The y-intercept is found by letting x = 0. The y-intercept is f102 = 1. Thex-intercepts are found by solving the equation f1x2 = 0. f1x2 = 0- 3x2 + 6x + 1 = 0 a = −3, b = 6, c = 1 The discriminant b2 - 4ac = 162 2 - 41 - 32 112 = 36 + 12 = 48 7 0, so theequation has two real solutions and the graph has two x-intercepts. Use thequadratic formula to find…
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The total annual revenue R of a certain resort hotel is related to the amount of money x the hotel spends on advertising its services by the function R(x) = −0.002x3 + 0.9x2 + 7x + 9,000 (0 ≤ x ≤ 400) where both R and x are measured in thousands of dollars. (a) Find the interval where the graph of R is concave upward. (Enter your answer using interval notation.) Find the interval where the graph of R is concave downward. (Enter your answer using interval notation.) What is the inflection point of the graph of R? (x, R(x)) = (b) Would it be more beneficial for the hotel to increase its advertising budget slightly when the budget is $140,000 or when it is $160,000? $140,000$160,000
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