Which of the following is/are true?

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Homework Help Overview

The discussion revolves around the classification of various geometric shapes in relation to their representation as functions, specifically focusing on straight lines, circles, and parabolas. The subject area is primarily related to functions and their graphical representations in mathematics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the validity of statements regarding straight lines, circles, and parabolas as functions, with an emphasis on the vertical line test. Questions arise about the implications of a parabola's axis of symmetry not being vertical.

Discussion Status

There is some agreement on the correctness of statement C, while statements A and B are questioned based on the vertical line test. A new perspective is introduced regarding the axis of symmetry of parabolas, leading to a reconsideration of the truth of all statements.

Contextual Notes

Participants are discussing the definitions and properties of functions as they relate to specific geometric shapes, with attention to the implications of the vertical line test and the orientation of parabolas.

Jaco Viljoen
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Homework Statement


A)
All straight lines are graphs of linear functions.

B)
All circles are graphs of quadratic functions.

C)
All parabolas are graphs of quadratic functions.

Homework Equations

The Attempt at a Solution


Only C is correct, due to the vertical line test, if A were a vertical line it would fail, and a circle will also fail.
 
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I will agree with you that only C is correct.

A vertical line is indeed not a function but is a straight line, therefore A will fail.
A circle has two y-coordinates for the x-value in the center (top and bottom). The vertical line test will indeed indicate a fail for it being a function.
A parabola only has one y-coordinate for a given x-value and will therefore pass the vertical line test and is therefore a function.
 
What if the axis of symmetry of the parabola is not vertical?
 
Oh yeah! I forgot about that one. Good thinking, Sammy!
In that case, none would be true.
 

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