Why does the vertical line test work?

Answer 1

#" "#
Please read the explanation.

#" "#
Let us say we have a graph drawn for a mathematical relation.

#color(red)(y=f(x)=x^2#

This is a mathematical relation, as for every value of #color(blue)(x#, there is a corresponding value of #color(blue)(y#.

To check whether this graph is a function, a Vertical Line Test can be used.

Let us examine the following graph drawn for the mathematical relation:

Can you observe the vertical lines drawn for various values of #color(red)(x# ?

All of these vertical lines intersect the graph at one point only.

If there is just one point of intersection,

that would mean,

for every x-value, there is just one unique y-value.

This property proves that the given mathematical relation

#color(red)(y=f(x)=x^2#

is a mathematical function.

Hence, the vertical line test works in determining whether a given relation is a function.

Let us try one more mathematical relation:

#color(blue)(y^2=-4x#

This mathematical relation creates a parabola and the parabola is symmetric about the x-axis, at #color(red)(y=0#.

This mathematical relation

#color(blue)(y^2=(-4x)# is NOT a function,

as the vertical line test fails.

Hope it helps.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The vertical line test works because it determines if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph fails the test and does not represent a function.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7