how many of the following are functions?

y= ±2x+7

y= √(5-x) (all under the rad)

y= 1/(x+62) - 2

y= -3^x + 41 (no parentheses around the -3 purposely)

i think they all are?

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- September 2nd 2013, 03:38 PMHell0simple function question
how many of the following are functions?

y= ±2x+7

y= √(5-x) (all under the rad)

y= 1/(x+62) - 2

y= -3^x + 41 (no parentheses around the -3 purposely)

i think they all are? - September 2nd 2013, 03:48 PMIdentityProblemRe: simple function question
The top equation doesn't look like a function. It has

*two*outputs for*one*input.

f(x) = y= ±2x+7

Example: f(2) = ±2(2)+7 = 11 and 3.

Graph it. It won't pass the vertical line test. A vertical line can pass through two points. - September 2nd 2013, 03:55 PMHell0Re: simple function question
- September 2nd 2013, 04:11 PMphys251Re: simple function question
Hell0,

1. What is the definition of a function?

2. What are some tests you can apply to check whether a relation is a function? - September 2nd 2013, 04:17 PMHell0Re: simple function question
- September 2nd 2013, 04:39 PMHell0Re: simple function question
ok so the first one is not. and the second one is not also. not sure about the bottom two

- September 2nd 2013, 04:52 PMIdentityProblemRe: simple function question
You can substitute in an arbitrary variable like

*a*into the equation**as the "input**."

This will lead to some**"output**."

**A function**can only have; otherwise, it is not a function.__one__unique output for every input

For example:

f(x) = y= ±2x+7

f(a) = ±2(a)+7 = -2a+7 and 2a+7. Those are*two*different outputs for that one input; hence, it is not a function.

For example:

f(x) = y= √(5-x)

f(a) = √(5-a) This leads to only one result; hence, it passes the test. This is a function. An input only gives one output.

-----

Another example:

x^{2}+ y^{2}= 1

Is that a function?

Algebraically, we can rewrite it by solving for y.

y^{2}= -x^{2}+ 1

±√(y^{2}) = ±√(-x^{2}+ 1)

y = ±√(-x^{2}+ 1)

This is not a function. The**±**tells us that there will be*two*outputs for a single input.

Again, you can put*a*in to make sure. y = ±√(-(a)^{2}+ 1) = +√(-(a)^{2}+ 1) and -√(-(a)^{2}+ 1) - September 2nd 2013, 04:58 PMHell0Re: simple function question
wow. and I got a 99 on the a2/trig regents last year. I'm embarrassed. I'll write back when I have an answer for the other two

- September 2nd 2013, 05:09 PMHell0Re: simple function question
1. no

2. yes

3. yes

4. yes

how did i do