Testing for Functions Represented Algebraically

[nycmathguy]

Section 1.4
Questions: 12, 14, 16, 18

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

12. x^2 - y = 9

- y = 9 - x^2

y = -9 + x^2

y = x^2 + 9

Yes, y is a function of x.

14. y = sqrt{x + 5}

Here we have y = a square root function with radicand x + 5.

I say y is a function of x.


16. ∣y∣ = 4 − x

Here we have the absolute value of y = 4 - x.
Not sure about this one.

18. x − 1 = 0

Solving for x, I get x = 1.
Although x = 1 is a vertical line passing through the point (1, 0), I do not see y anywhere EXCEPT that clearly y = 0.

The equation x - 1 = 0 does not represent y as a function of x.

You say?

 

[MathLover1]

correct!

 

[nycmathguy]

correct!

Is 16 right?

 

[MathLover1]

16. ∣y∣ = 4 − x is not a function, does not pass vertical line test
see attached

 

[nycmathguy]

16. ∣y∣ = 4 − x is not a function, does not pass vertical line test
see attached

The graph helps to see that it is not a function. I sure would like to see more people participate here but perhaps this is too much to ask for.