Concept explainers
In Exercises 1–6, use the given rational function to find the indicated function values. If a Function value does not exist, so state.
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EBK INTERMEDIATE ALGEBRA FOR COLLEGE ST
- The function f: RR defined by f(x) = 5x³ + 3x² - x + 7 is O(x). O True Falsearrow_forwardWhich function is increasing as x approaches negative infinity and decreasing as x approaches positive infinity? Select all that apply. Select all that apply: O f(x) = -4x (x +2)(x - 1) %3D O f(x) = -¤(x + 5)(x – 9)(x+ 2) O f(x)= (2x+ 7)(3x – 1)(x +5)(x - 7) | O f(x)= -3r² (3x + 5)(2x – 1)(x + 3)(x – 5) | %3D O f(x) = -x(3x – 2)(2x + 7)(x + 5)(x – 1) |arrow_forwardAnalyze the graphs of b(x), c(x), d(x), and f(x). Write each function in terms of the indicated function. 100 ugu cux) bx ax A. Write b(x) in terms of f(x). b(x) = B. Write c(x) in terms of f(x). c(x) = C. Write d(x) in terms of b(x). d(x) D. Write b(x) in terms of c(x). b(x) = Darrow_forward
- In Exercises 43 and 44, graph the functions. Notice in each case that the numerator and denominator contain at least one com- mon factor. Thus you can simplify each quotient; but don't lose track of the domain of the function as it was initially defined. x + 2 x² - 4 43. (a) y (b) y = (c) y = X + 2 X-2 X-1 (x - 1)(x-2)arrow_forwardDetermine if the functions in each pair are equivalent. Provide mathematical proof or justification for your answer – algebraic or by substituting x = 0. a) f (x) = (-5x² + 100x + 1000) – (-5x² + 75x + 1200) and g(x) = 25x – 200 b) f(x) = (2x – 1) + (x – 2) – (x – 3) and g(x) = (3x – 2) – (2x + 3) – (-x – 1)arrow_forwardThe function h is defined by h (x) = 2x-1. Find h (2a). h(2a) = 0arrow_forward
- The function f (x) undergoes a vertical compression by a factor of, a horizontal shift left 4 units, and a vertical shift down 2 units to become g(x). Which equation describes g (x)? ○ g(x) = 3x + 4| – 2 ○ g(x) = |x g(x) = ○ g(x) = T 4+2 |x 4| 2 x + 4 + 2arrow_forwardSketch the graph of f.arrow_forwardExpress each function as a composition of two functions. (Find f(x) and g(x) such that the given function equals (fog)(x). Assume g(x) ‡ x.) (a) F(x) = √√√7x + 6 {f(x), g(x)} = (b) G(x) = 18x 71 {f(x), g(x)} = (c) H(x) = (ax + b)² {f(x), g(x)} = (d) T(x) = 1/√x {f(x), g(x)} =arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning