Question

Can someone explain to me how to relate a vertical line test to understanding functions?

Answer 1

Sure, what do you not understand though?

Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

See my answer to a similar question earlier today - http://openstudy.com/users/ybarrap#/updates/5574cbc8e4b01d0053ac2507

Answer 6

This is because you have two \(x\) values.

Answer 7

*multiple

Answer 8

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

Answer 9

like this
and ofc not a perfect graph lel :P:P

Answer 10

It can't pass through two POINTS.

Answer 11

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.

Answer 12

i get it.

Answer 13

All right, just wanted to make sure.

Answer 14

vertical line means no slope

Answer 15

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

Answer 16

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

Answer 17

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.)

Answer 18

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'

Answer 19

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.

Answer 20

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

Answer 21

Thank you, @ybarrap