A Function of x

[nycmathguy]

In Exercises 11–18, determine whether the equation represents y as a function of x.

We are looking for y = a bunch of stuff with x on this side.

12. x^2 − y = 9

14. y = sqrt{x + 5}

16. | y | = 4 - x

18. x - 1 = 0

Let me see.

For (12), isolating y, I get y = x^2 - 9. I say the equation represents y as a function of x.

For (14), This equation clearly shows y as a function of x.

I am not too sure about 16. The | y | throws me into a loop.

For (18), after adding 1 to both sides, I get x = 1, which is a vertical line going through the point
(1, 0). The line x = 1 does not represent y as a function of x.

You say?

 

[MathLover1]

In Exercises 11–18, determine whether the equation represents y as a function of x.

We are looking for y = a bunch of stuff with x on this side.

12. x^2 − y = 9

14. y = sqrt{x + 5}

16. | y | = 4 - x

18. x - 1 = 0

Let me see.

For (12), isolating y, I get y = x^2 - 9. I say the equation represents y as a function of x.

For (14), This equation clearly shows y as a function of x.

I am not too sure about 16. The | y | throws me into a loop.

For (18), after adding 1 to both sides, I get x = 1, which is a vertical line going through the point
(1, 0). The line x = 1 does not represent y as a function of x.

You say?

To be a function, it has to pass the "vertical line test" which means for each x-value there is at most one y-value.

you can see from the graph if the function pass the "vertical line test"

12. x^2 − y = 9-> parabola that open upwards, is a function

let use vertical line x=3 to see that the function pass the "vertical line test"



All parabolas are not functions. Only parabolas that open upwards or downwards are considered functions. Parabolas that open left or right are not considered parabolas. You can test whether or not a parabola is considered a function by conducting the "Vertical Line Test."


14. y = sqrt(x + 5)
is a function



16. | y | = 4 - x
vertical line test:
not a function


18. x - 1 = 0-> vertical line, your answer is correct

 

[nycmathguy]

To be a function, it has to pass the "vertical line test" which means for each x-value there is at most one y-value.

you can see from the graph if the function pass the "vertical line test"

12. x^2 − y = 9-> parabola that open upwards, is a function

let use vertical line x=3 to see that the function pass the "vertical line test"



All parabolas are not functions. Only parabolas that open upwards or downwards are considered functions. Parabolas that open left or right are not considered parabolas. You can test whether or not a parabola is considered a function by conducting the "Vertical Line Test."


14. y = sqrt(x + 5)
is a function



16. | y | = 4 - x
vertical line test:
not a function


18. x - 1 = 0-> vertical line, your answer is correct

1. Great reply that will not be allowed at the other site.

2. Parabolas that open to the right and left fail the vertical line test.

3. Want to stay here (just the two of us) or continue at the other site? Please, pick one site.

4. Disregarding 3 above, we can also do this:

A. Stay here for the rest of precalculus.

B. Use the other math site for another course like geometry, trigonometry, college algebra, or probability.

5. Suggestion:

A. Stay here for the rest of precalculus.

B. Use the other site for a course that coincides with precalculus.

Considering that I need to greatly polish my algebra skills before stepping into calculus 1, why not study college algebra at the other site and precalculus here?

You say?

P. S. You are not going to find another math enthusiast like me in the current century, honestly.

Extra:

Is it possible to send an invitation e-mail to other math enthusiasts at algebra.com? In other words, the SAME E-MAIL to fellow math people to join us here or at mathforums.com.

You say?