Which of the following is/are true?

  • Thread starter Thread starter Jaco Viljoen
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AI Thread Summary
Only statement C is correct, as all parabolas are indeed graphs of quadratic functions. Statement A fails because vertical lines do not qualify as functions, while statement B fails since circles have two y-coordinates for a single x-value, violating the vertical line test. The discussion emphasizes the importance of the vertical line test in determining whether a graph represents a function. Additionally, if a parabola's axis of symmetry is not vertical, it raises further considerations about the validity of the statements. Ultimately, the consensus is that only C holds true.
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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