# simple function question

• Sep 2nd 2013, 03:38 PM
Hell0
simple 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?
• Sep 2nd 2013, 03:48 PM
IdentityProblem
Re: 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.
• Sep 2nd 2013, 03:55 PM
Hell0
Re: simple function question
Quote:

Originally Posted by IdentityProblem
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.

thanks ill try that. how can i algebraically check for the other ones?
• Sep 2nd 2013, 04:11 PM
phys251
Re: 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?
• Sep 2nd 2013, 04:17 PM
Hell0
Re: simple function question
Quote:

Originally Posted by phys251
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?

haha I can graph it I know. but the pictures aren't so clear and I'm not good at changing the view
• Sep 2nd 2013, 04:39 PM
Hell0
Re: simple function question
ok so the first one is not. and the second one is not also. not sure about the bottom two
• Sep 2nd 2013, 04:52 PM
IdentityProblem
Re: simple function question
Quote:

Originally Posted by Hell0
thanks ill try that. how can i algebraically check for the other ones?

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 one unique output for every input; otherwise, it is not a function.

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:
x2 + y2 = 1
Is that a function?
Algebraically, we can rewrite it by solving for y.
y2 = -x2 + 1
±√(y2) = ±√(-x2 + 1)
y = ±√(-x2 + 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)
• Sep 2nd 2013, 04:58 PM
Hell0
Re: 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
• Sep 2nd 2013, 05:09 PM
Hell0
Re: simple function question
1. no
2. yes
3. yes
4. yes

how did i do