Which of the following is/are true?

  • #1
160
9

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.
 

Answers and Replies

  • #2
27
1
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.
 
  • #3
SammyS
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What if the axis of symmetry of the parabola is not vertical?
 
  • #4
27
1
Oh yeah! I forgot about that one. Good thinking, Sammy!
In that case, none would be true.
 

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