## anonymous one year ago Can someone explain to me how to relate a vertical line test to understanding functions?

1. anonymous

Sure, what do you not understand though?

2. Nnesha

just draw vertical lines if graph of the function hit the vertical lien more than one spot then that graph doesn't represent a function ???q

3. anonymous

I'm not sure how to explain it really. Doesn't the line have to go through a function, like a U shape, or something like that? I just need a better way of understanding it.

4. anonymous

Imagine a graph, that has a equation that looks like a U when graphed. This equation would be a function. If the equation when graphed looked like a Z it would not pass the vertical line test.

5. ybarrap

6. anonymous

This is because you have two $$x$$ values.

7. anonymous

*multiple

8. anonymous

So it cant pass through two lines, right? Ok, thank you!

9. Nnesha

|dw:1433726425861:dw| like this and ofc not a perfect graph lel :P:P

10. ybarrap

It can't pass through two POINTS.

11. anonymous

Okay so tell me does this graph pass the vertical line test, and is it a function: $f\left(x\right)\ =\ 5x^2\ +\ 2$ You can use: https://www.desmos.com/calculator to graph.

12. anonymous

i get it.

13. anonymous

All right, just wanted to make sure.

14. triciaal

vertical line means no slope

15. anonymous

can you explain the inputs & outputs when graphing a function? I never got it.

16. triciaal

true you don't have a function if you have more than one output for a given input

17. anonymous

By inputs, and outputs when graphing a function do you mean something like this: $f(x) = 5x + 1$ $f(5) = 5x + 1 \rightarrow f(5) = 5(5) + 1 = 26$ So a point you would graph would be $$(5, 26)$$. Basically you keep feeding in $$x$$ values to get $$y$$ values to graph you equation. (The line would go through the points, you plot down.)

18. anonymous

How would I go about something like this? 'Determine if the outside temperature is a function of the time of day or if the time of day is a function of temperature'

19. ybarrap

The question about temperature and time is is about identifying the independent variable. The independent variable is not a function of anything. The thing measured, in this case, temperature, is a function of time. So here time would be the x-axis and temperature would be the y-axis. You give me the time, I give you a unique temperature. The other way around, if I give you a temperature, there could be multiple times of day where the temperature could be that value. So temperature could NOT be a function for that reason. Usually you want to know what the temperature will be at a certain time of day;. This is another way you know that temperature is a function of time.

20. triciaal

a simple question "which variable is controlled?" the controlled variable is the independent variable. The one that varies is the output, the dependent variable.

21. anonymous

Thank you, @ybarrap

22. triciaal

|dw:1433731436123:dw|

23. ybarrap

You're welcome @Kitt020912 .