a. Explanation Given information: A function is given as, f ( x ) = x 2 + x − 1 . Three lines are given as, y = x + 3 y = x − 1 and y = x − 3 Calculation: Three lines are given as, y = x + 3 ... eq(i) y = x − 1 ... eq(ii) and y = x − 3 ... eq(iii) Given function is, f ( x ) = x 2 + x − 1 . Let us suppose, y = f ( x ) = x 2 + x − 1 ....eq(iv) If the line y = x + 3 passes through the graph of function f ( x ) , then upon solving eq(i) and eq(iv) will give the point of intersection. Substituting y = x + 3 in eq(iv), y = x 2 + x − 1 ⇒ x + 3 = x 2 + x − 1 ⇒ x 2 = 4 ⇒ x = ± 2 From eq(i) y = x + 3 , when x = 2 , then y = 2 + 3 = 5 when x = − 2 , then y = − 2 + 3 = 1 Therefore, point of intersection will be ( 2 , 5 ) and ( − 2 , 1 ) Again, if the line y = x − 3 passes through the graph of function f ( x ) , then upon solving eq(ii) and eq(iv) will give the point of intersection b. To determine The sketch of function f and three given lines. c. To determine The relationship between graph of f and the lines y = x + c as c changes from − ∞ to ∞ .

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 1.2, Problem 50E

To determine

If the lines y=x+3,y=x−1, and y=x−3 intersect the graph of f in two, one, and zero points respectively.

To determine

The sketch of function f and three given lines.

To determine

The relationship between graph of f and the lines y=x+c as c changes from −∞ to ∞ .

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Chapter 1.2, Problem 49E

Chapter 1.2, Problem 51E

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Chapter 1 Solutions

CALCULUS (CLOTH)

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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If the lines y = x + 3 , y = x − 1 , and y = x − 3 intersect the graph of f in two, one, and zero points respectively.

Solution Summary: The author explains that f(x)=x2+x-1 intersects the graph in two, one, and zero points.

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If the lines y=x+3,y=x−1, and y=x−3 intersect the graph of f in two, one, and zero points respectively.

The sketch of function f and three given lines.

The relationship between graph of f and the lines y=x+c as c changes from −∞ to ∞ .

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Chapter 1 Solutions