Math / Algebra

QuestionUse the table to determine if $f$ is one-to-one. \begin{tabular}{|r|l|l|l|l|} \hline $x$ & -3 & -6 & -5 & -2 \\ \hline $f(x)$ & -2 & -4 & -2 & -1 \\ \hline \end{tabular}
Is f one-to-one? No Yes

Studdy Solution

STEP 1

What is this asking? Does every input ( $x$ ) in our table have a unique output ( $f(x)$ )? Watch out! Don't get tricked!
Just because different inputs can have the same output doesn't mean they always do.
We need to check all the inputs and outputs in the table.

STEP 2

1. Check for duplicate outputs.
2. Determine if the function is one-to-one.

STEP 3

Let's scan the $f(x)$ row in our table.
We're looking for any repeats, any outputs that show up more than once.
Do you see any?
I see a -2 appearing twice!

STEP 4

Specifically, $f(-3) = -2$ and $f(-5) = -2$ .
This means two different inputs, $-3$ and $-5$ , give us the same output, $-2$ .

STEP 5

A function is one-to-one if every input has exactly one output, and every output has exactly one input.
It's like a perfect matching game!

STEP 6

Since we found two inputs, $-3$ and $-5$ , that both produce the same output, $-2$ , this function breaks the one-to-one rule.
It's like having two left shoes for the same right foot!

STEP 7

No, $f$ is not one-to-one.

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QuestionUse the table to determine if $f$ is one-to-one. \begin{tabular}{|r|l|l|l|l|} \hline $x$ & -3 & -6 & -5 & -2 \\ \hline $f(x)$ & -2 & -4 & -2 & -1 \\ \hline \end{tabular}
Is f one-to-one? No Yes

Studdy Solution

STEP 1

What is this asking? Does every input ( $x$ ) in our table have a unique output ( $f(x)$ )? Watch out! Don't get tricked!
Just because different inputs can have the same output doesn't mean they always do.
We need to check all the inputs and outputs in the table.

STEP 2

1. Check for duplicate outputs.
2. Determine if the function is one-to-one.

STEP 3

Let's scan the $f(x)$ row in our table.
We're looking for any repeats, any outputs that show up more than once.
Do you see any?
I see a -2 appearing twice!

STEP 4

Specifically, $f(-3) = -2$ and $f(-5) = -2$ .
This means two different inputs, $-3$ and $-5$ , give us the same output, $-2$ .

STEP 5

A function is one-to-one if every input has exactly one output, and every output has exactly one input.
It's like a perfect matching game!

STEP 6

Since we found two inputs, $-3$ and $-5$ , that both produce the same output, $-2$ , this function breaks the one-to-one rule.
It's like having two left shoes for the same right foot!

STEP 7

No, $f$ is not one-to-one.

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QuestionUse the table to determine if fff is one-to-one. \begin{tabular}{|r|l|l|l|l|} \hlinexxx & -3 & -6 & -5 & -2 \\ \hlinef(x)f(x)f(x) & -2 & -4 & -2 & -1 \\ \hline \end{tabular}Is f one-to-one? No Yes

Studdy Solution

STEP 1

What is this asking? Does every input (xxx) in our table have a unique output (f(x)f(x)f(x))? Watch out! Don't get tricked!Just because different inputs *can* have the same output doesn't mean they *always* do.We need to check *all* the inputs and outputs in the table.

STEP 2

1. Check for duplicate outputs.2. Determine if the function is one-to-one.

STEP 3

Let's **scan** the f(x)f(x)f(x) row in our table.We're looking for any repeats, any outputs that show up more than once.Do you see any?I see a **-2** appearing twice!

STEP 4

Specifically, f(−3)=−2f(-3) = -2f(−3)=−2 and f(−5)=−2f(-5) = -2f(−5)=−2.This means two different inputs, −3-3−3 and −5-5−5, give us the same output, −2-2−2.

STEP 5

A function is **one-to-one** if every input has *exactly* one output, and every output has *exactly* one input.It's like a perfect matching game!

STEP 6

Since we found two inputs, −3-3−3 and −5-5−5, that both produce the same output, −2-2−2, this function breaks the one-to-one rule.It's like having two left shoes for the same right foot!

STEP 7

No, fff is *not* one-to-one.

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Start learning now

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QuestionUse the table to determine if $f$ is one-to-one. \begin{tabular}{|r|l|l|l|l|} \hline $x$ & -3 & -6 & -5 & -2 \\ \hline $f(x)$ & -2 & -4 & -2 & -1 \\ \hline \end{tabular}
Is f one-to-one? No Yes

What is this asking? Does every input ( $x$ ) in our table have a unique output ( $f(x)$ )? Watch out! Don't get tricked!
Just because different inputs can have the same output doesn't mean they always do.
We need to check all the inputs and outputs in the table.

1. Check for duplicate outputs.
2. Determine if the function is one-to-one.

Let's scan the $f(x)$ row in our table.
We're looking for any repeats, any outputs that show up more than once.
Do you see any?
I see a -2 appearing twice!

Specifically, $f(-3) = -2$ and $f(-5) = -2$ .
This means two different inputs, $-3$ and $-5$ , give us the same output, $-2$ .

A function is one-to-one if every input has exactly one output, and every output has exactly one input.
It's like a perfect matching game!

Since we found two inputs, $-3$ and $-5$ , that both produce the same output, $-2$ , this function breaks the one-to-one rule.
It's like having two left shoes for the same right foot!

No, $f$ is not one-to-one.