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3 Express each function in the form a(x + b)2 +c, where a b and c are constants and hence state the range of each function. a f(x) = x² + 4x - 1 for x = R

3 Express each function in the form a(x + b)2 +c, where a b and c are constants and hence state the range of each function. a f(x) = x² + 4x - 1 for x = R

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 51E
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Please help me answer questions 3.A, 4.A, 5, 6, and 7

3 a b d f: x = 1+ √2x - 1 for x ≥ 0.5 Express each function in the form a(x + b)² + c, where a b and c are constants and hence state the range of each function. 7 f(x) a er 4 Express each function in the form a – b(x + c)², where a, b and c are constants and hence state the range of each function. a f(x) = 3 - 2x x² for x ER b f(x) x² for x ER — 5 The function g : x ↔ 6 + 3ax − 3x², where a is a constant is defined for x € R. Find the range of g in terms of a. 6 f(x) = x² 4 for x ER, -a ≤ x ≤ a b C uj f(x) = x² + 4x − 1 for x = R f(x) f(x) = 2x² 4x + 3 for x ER = 154 If the range of the function f is −4 ≤ f(x) < 5, find the value of a. f(x) = 4x² = R,0 < x < k Express f(x) in the form a (x +6²) + c. State the value of k for which the graph of y = f(x) has a line of symmetry. For your value of k from part b, find the range of f. 1 - 6x 4x² - 8x + 2 for x € E TIP If we draw all possible vertical lines on the graph of a mapping, the mapping is: a function if each line cuts the graph no more than
Transcribed Image Text:3 a b d f: x = 1+ √2x - 1 for x ≥ 0.5 Express each function in the form a(x + b)² + c, where a b and c are constants and hence state the range of each function. 7 f(x) a er 4 Express each function in the form a – b(x + c)², where a, b and c are constants and hence state the range of each function. a f(x) = 3 - 2x x² for x ER b f(x) x² for x ER — 5 The function g : x ↔ 6 + 3ax − 3x², where a is a constant is defined for x € R. Find the range of g in terms of a. 6 f(x) = x² 4 for x ER, -a ≤ x ≤ a b C uj f(x) = x² + 4x − 1 for x = R f(x) f(x) = 2x² 4x + 3 for x ER = 154 If the range of the function f is −4 ≤ f(x) < 5, find the value of a. f(x) = 4x² = R,0 < x < k Express f(x) in the form a (x +6²) + c. State the value of k for which the graph of y = f(x) has a line of symmetry. For your value of k from part b, find the range of f. 1 - 6x 4x² - 8x + 2 for x € E TIP If we draw all possible vertical lines on the graph of a mapping, the mapping is: a function if each line cuts the graph no more than
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