## Which of the following are functions? f=x+5, f=3 if x>2,

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
isabelrachel
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### Which of the following are functions? f=x+5, f=3 if x>2,

Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.

Iam thinking for problem (a) that it is a FUNCTION because the value could be any number in X for example x can = any variable as long as it’s a single value for instance 3 so hmmmm f(3)=3+5 I think I don’t know for sure 3 being the single variable if x={1,2,3,4,5} I AM LOST. What do you think?

I think they are all functions.

a. f(x) = x + 5
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0

jaybird0827
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### Re: FUNCTIONS

Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.

Iam thinking for problem (a) that it is a FUNCTION because the value could be any number in X for example x can = any variable as long as it’s a single value for instance 3 so hmmmm f(3)=3+5 I think I don’t know for sure 3 being the single variable if x={1,2,3,4,5} I AM LOST. What do you think?

I think they are all functions.

a. f(x) = x + 5
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
For a relation to be a function there has to be one and only one output value $f(x)$ per input $x$. I agree with your answer for a.

Let's look at b. As long as your input $x$ never results in more than one output $f(x)$. For example, let $x\,=\,-5$. According to the rule, $f(-5)\,=\,-2$, right? $f(-5)$ does not equal anything but $-2$. What do think now?

What about c? Look at the last clause. Doesn't that mean that I could input 0 and get 7, or I could input 0 and get -7? How is this example different from a and b?

Does this help. If not, please reply and show how far you've gotten. Oh, and click here for a really good explanation of functions -> http://www.purplemath.com/modules/fcns.htm

stapel_eliz
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I think they are all functions.
Follow the link (provided earlier) to study the basic definition of "function": for any input x, there can be one and only one output y.

jaybird0827
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### Re: Which of the following are functions? f=x+5, f=3 if x>2,

Subject: Which of the following are functions? f=x+5, f=3 if x>2,
Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.

Iam thinking for problem (a) that it is a FUNCTION because the value could be any number in X for example x can = any variable as long as it’s a single value for instance 3 so hmmmm f(3)=3+5 I think I don’t know for sure 3 being the single variable if x={1,2,3,4,5} I AM LOST. What do you think?

I think they are all functions.

a. f(x) ==
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
For a relation to be a function there has to be one and only one output value $f(x)$ per input $x$. I agree with your answer for a.

Let's look at b. As long as your input $x$ never results in more than one output $f(x)$. For example, let $x\,=\,-5$. According to the rule, $f(-5)\,=\,-2$, right? $f(-5)$ does not equal anything but $-2$. What do think now?

What about c? Look at the last clause. Doesn't that mean that I could input 0 and get 7, or I could input 0 and get -7? How is this example different from a and b?

Does this help. If not, please reply and show how far you've gotten. Oh, and click here for a really good explanation of functions -> http://www.purplemath.com/modules/fcns.htm

Ok now iam really confused. On part B.f(x) = 3 if x>2 otherwise f(x) = -2
Are those three seperate functions that i have to solve for example

f(x)=3

x>2

f(x)=-2 X=-5 The one you did
Part B is one relation. Your job is to decide whether the conditions in part B comprise a function. It might help to consider ordered pairs where the first number is your input $x$ the second number is the output specified by the relation.

First, let's clarify: f(x) = 3 if x>2 otherwise f(x) = -2 means all of the following:

$f(x)\,=\,3\,when\,x\,\gt\,2$
$f(x)\,=\,-2\,when\,x\,\le\,2$

Examples of ordered pairs, 1st condition: $(2.1,3),\,(3,3),\,(10,3),\,(50\,000,3)$. If my input $x$ is any number greater than $2$, my output is always $3$. We cannot list all possible ordered pairs that meet this condition; there are infinitely many such pairs.

Examples of ordered pairs, 2nd condition: $(2,-2),\,(1.9,-2)\,(0,-2),\,(-10,-2),\,(-50\,000,-2)$. If my input $x$ is $2$ or any number less than $2$, my output is always $-2$. Again, there are infinitely many such ordered pairs that meet this condition.

The relation in B is a function because there is one and only one output given any $x$.

If the conditions were such that I could generate, $(5,3)$ and $(5,-2)$ it would not be a function because more than one output is possible given the same input. But $(5,-2)$ is not valid because the above conditions state that when $x$ is a number greater than 2, the output has to be 3.