Math / Algebra

QuestionA relation in $x$ and $y$ is given. Determine if the relation defines $y$ as a one-to-one function of $x$ . The relation defines $y$ as a one-to-one function of $x$ . The relation does not define $y$ as a one-to-one function of $x$ .

Studdy Solution

STEP 1

What is this asking? Does each $x$ value go to only one $y$ value, and does each $y$ value come from only one $x$ value? Watch out! It's easy to mix up "one-to-one" with just being a function!
A function just needs each $x$ to go to one $y$ , but one-to-one is stricter!

STEP 2

1. Check if it's a function
2. Check if it's one-to-one

STEP 3

Alright, let's check if this relation is a function!
Does each $x$ value have only one corresponding $y$ value?
Looking at our diagram, we see that $14$ goes to both $3$ and $6$ .
Uh oh!
That's a problem!

STEP 4

Since $14$ is going to two different $y$ values, this is not a function.
It's like a mischievous little $x$ trying to sneak into two parties at once!

STEP 5

Even though it's not a function, let's check the one-to-one condition anyway, just for kicks!
Does each $y$ value have only one corresponding $x$ value?

STEP 6

Well, $3$ comes from $14$ , $6$ comes from $14$ , and $9$ comes from $22$ .
So, $3$ and $6$ both come from the same $x$ value!
That breaks the one-to-one rule.

STEP 7

This relation is not a one-to-one function.
In fact, it's not a function at all!
It breaks the rules in two ways: $14$ maps to two different $y$ values, and both $3$ and $6$ map back to the same $x$ value.

Was this helpful?

QuestionA relation in $x$ and $y$ is given. Determine if the relation defines $y$ as a one-to-one function of $x$ . The relation defines $y$ as a one-to-one function of $x$ . The relation does not define $y$ as a one-to-one function of $x$ .

Studdy Solution

STEP 1

What is this asking? Does each $x$ value go to only one $y$ value, and does each $y$ value come from only one $x$ value? Watch out! It's easy to mix up "one-to-one" with just being a function!
A function just needs each $x$ to go to one $y$ , but one-to-one is stricter!

STEP 2

1. Check if it's a function
2. Check if it's one-to-one

STEP 3

Alright, let's check if this relation is a function!
Does each $x$ value have only one corresponding $y$ value?
Looking at our diagram, we see that $14$ goes to both $3$ and $6$ .
Uh oh!
That's a problem!

STEP 4

Since $14$ is going to two different $y$ values, this is not a function.
It's like a mischievous little $x$ trying to sneak into two parties at once!

STEP 5

Even though it's not a function, let's check the one-to-one condition anyway, just for kicks!
Does each $y$ value have only one corresponding $x$ value?

STEP 6

Well, $3$ comes from $14$ , $6$ comes from $14$ , and $9$ comes from $22$ .
So, $3$ and $6$ both come from the same $x$ value!
That breaks the one-to-one rule.

STEP 7

This relation is not a one-to-one function.
In fact, it's not a function at all!
It breaks the rules in two ways: $14$ maps to two different $y$ values, and both $3$ and $6$ map back to the same $x$ value.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA relation in xxx and yyy is given. Determine if the relation defines yyy as a one-to-one function of xxx. The relation defines yyy as a one-to-one function of xxx. The relation does not define yyy as a one-to-one function of xxx.

Studdy Solution

STEP 1

What is this asking? Does each xxx value go to only *one* yyy value, and does each yyy value come from only *one* xxx value? Watch out! It's easy to mix up "one-to-one" with just being a function!A function just needs each xxx to go to one yyy, but one-to-one is stricter!

STEP 2

1. Check if it's a function2. Check if it's one-to-one

STEP 3

Alright, let's **check if this relation is a function**!Does each xxx value have only *one* corresponding yyy value?Looking at our diagram, we see that 141414 goes to both 333 and 666.Uh oh!That's a problem!

STEP 4

Since 141414 is going to *two* different yyy values, this is *not* a function.It's like a mischievous little xxx trying to sneak into two parties at once!

STEP 5

Even though it's not a function, let's **check the one-to-one condition** anyway, just for kicks!Does each yyy value have only *one* corresponding xxx value?

STEP 6

Well, 333 comes from 141414, 666 comes from 141414, and 999 comes from 222222.So, 333 and 666 both come from the same xxx value!That breaks the one-to-one rule.

STEP 7

This relation is *not* a one-to-one function.In fact, it's not a function at all!It breaks the rules in two ways: 141414 maps to two different yyy values, and both 333 and 666 map back to the same xxx value.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA relation in $x$ and $y$ is given. Determine if the relation defines $y$ as a one-to-one function of $x$ . The relation defines $y$ as a one-to-one function of $x$ . The relation does not define $y$ as a one-to-one function of $x$ .

What is this asking? Does each $x$ value go to only one $y$ value, and does each $y$ value come from only one $x$ value? Watch out! It's easy to mix up "one-to-one" with just being a function!
A function just needs each $x$ to go to one $y$ , but one-to-one is stricter!

1. Check if it's a function
2. Check if it's one-to-one

Alright, let's check if this relation is a function!
Does each $x$ value have only one corresponding $y$ value?
Looking at our diagram, we see that $14$ goes to both $3$ and $6$ .
Uh oh!
That's a problem!

Since $14$ is going to two different $y$ values, this is not a function.
It's like a mischievous little $x$ trying to sneak into two parties at once!

Even though it's not a function, let's check the one-to-one condition anyway, just for kicks!
Does each $y$ value have only one corresponding $x$ value?

Well, $3$ comes from $14$ , $6$ comes from $14$ , and $9$ comes from $22$ .
So, $3$ and $6$ both come from the same $x$ value!
That breaks the one-to-one rule.

This relation is not a one-to-one function.
In fact, it's not a function at all!
It breaks the rules in two ways: $14$ maps to two different $y$ values, and both $3$ and $6$ map back to the same $x$ value.