Textbook Question
Provide a short answer to each question. What is the domain of the function ƒ(x)=1/x? What is its range?
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Ch. 3 - Polynomial and Rational Functions
Chapter 4, Problem 3
Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Parabola
A parabola is a symmetrical, U-shaped curve that can open either upwards or downwards. It is defined by a quadratic function of the form y = ax^2 + bx + c, where 'a' determines the direction of the opening. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.
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Horizontal Parabolas
Vertex
The vertex of a parabola is the highest or lowest point on its graph, depending on the direction it opens. For a parabola that opens downwards, the vertex represents the maximum point. The coordinates of the vertex can be found using the formula (-b/2a, f(-b/2a)) for the quadratic function.
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08:07Vertex Form
Maximum and Minimum Values
In the context of parabolas, the maximum value occurs at the vertex for parabolas that open downwards, while the minimum value occurs at the vertex for those that open upwards. Understanding these values is crucial for analyzing the behavior of quadratic functions and their graphs.
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02:44Maximum Turning Points of a Polynomial Function
Related Practice
Textbook Question
Determine whether each statement is true or false. If false, explain why. Because x-1 is a factor of ƒ(x)=x^6-x^4+2x^2-2, we can also conclude that ƒ(1)=0
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Textbook Question
Determine whether each statement is true or false. If false, explain why. For ƒ(x)=(x+2)^4(x-3), the number 2 is a zero of multiplicity 4.
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1
rank
Textbook Question
Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x^2-12x-1
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Textbook Question
Determine whether each statement is true or false. If false, explain why. A polynomial function having degree 6 and only real coefficients may have no real zeros.
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Textbook Question
Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .
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