Math / Algebra

QuestionDetermine whether the function is one-to-one. $f(x)=|x+4|$
Is the function one-to-one? Yes No

Studdy Solution

STEP 1

What is this asking? Is there only one $x$ value for every $y$ value in the function $f(x) = |x+4|$ ? Watch out! Absolute value functions can be tricky!
Remember they create "V" shapes and that can lead to the same $y$ value for different $x$ values.

STEP 2

1. Understand One-to-One
2. Test the Function

STEP 3

A one-to-one function means that for every $y$ value, there's only one $x$ value that can produce it.
Think of it like a special club where each member has a unique secret code.
No two members share the same code!

STEP 4

Let's pick a positive number for $f(x)$ , say $f(x) = 2$ .

STEP 5

$|x+4| = 2$ This means $x+4$ could equal positive 2 or negative 2.

STEP 6

If $x+4 = 2$ , then $x = 2 - 4 = \mathbf{-2}$ .

STEP 7

If $x+4 = -2$ , then $x = -2 - 4 = \mathbf{-6}$ .

STEP 8

Whoa! We found two different $x$ values ( $-2$ and $-6$ ) that give us the same $f(x)$ value of $2$ .
This breaks our "one $x$ for every $y$ " rule!

STEP 9

No, the function $f(x) = |x+4|$ is not one-to-one.

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QuestionDetermine whether the function is one-to-one. $f(x)=|x+4|$
Is the function one-to-one? Yes No

Studdy Solution

STEP 1

What is this asking? Is there only one $x$ value for every $y$ value in the function $f(x) = |x+4|$ ? Watch out! Absolute value functions can be tricky!
Remember they create "V" shapes and that can lead to the same $y$ value for different $x$ values.

STEP 2

1. Understand One-to-One
2. Test the Function

STEP 3

A one-to-one function means that for every $y$ value, there's only one $x$ value that can produce it.
Think of it like a special club where each member has a unique secret code.
No two members share the same code!

STEP 4

Let's pick a positive number for $f(x)$ , say $f(x) = 2$ .

STEP 5

$|x+4| = 2$ This means $x+4$ could equal positive 2 or negative 2.

STEP 6

If $x+4 = 2$ , then $x = 2 - 4 = \mathbf{-2}$ .

STEP 7

If $x+4 = -2$ , then $x = -2 - 4 = \mathbf{-6}$ .

STEP 8

Whoa! We found two different $x$ values ( $-2$ and $-6$ ) that give us the same $f(x)$ value of $2$ .
This breaks our "one $x$ for every $y$ " rule!

STEP 9

No, the function $f(x) = |x+4|$ is not one-to-one.

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QuestionDetermine whether the function is one-to-one. f(x)=∣x+4∣f(x)=|x+4|f(x)=∣x+4∣Is the function one-to-one? Yes No

Studdy Solution

STEP 1

What is this asking? Is there only one xxx value for every yyy value in the function f(x)=∣x+4∣f(x) = |x+4|f(x)=∣x+4∣? Watch out! Absolute value functions can be tricky!Remember they create "V" shapes and that can lead to the same yyy value for different xxx values.

STEP 2

1. Understand One-to-One2. Test the Function

STEP 3

A **one-to-one** function means that for every yyy value, there's only one xxx value that can produce it.Think of it like a special club where each member has a unique secret code.No two members share the same code!

STEP 4

Let's pick a **positive** number for f(x)f(x)f(x), say f(x)=2f(x) = 2f(x)=2.

STEP 5

∣x+4∣=2 |x+4| = 2 ∣x+4∣=2 This means x+4x+4x+4 could equal **positive 2** or **negative 2**.

STEP 6

If x+4=2x+4 = 2x+4=2, then x=2−4=−2x = 2 - 4 = \mathbf{-2}x=2−4=−2.

STEP 7

If x+4=−2x+4 = -2x+4=−2, then x=−2−4=−6x = -2 - 4 = \mathbf{-6}x=−2−4=−6.

STEP 8

Whoa! We found **two different** xxx values (−2-2−2 and −6-6−6) that give us the same f(x)f(x)f(x) value of 222.This breaks our "one xxx for every yyy" rule!

STEP 9

No, the function f(x)=∣x+4∣f(x) = |x+4|f(x)=∣x+4∣ is **not one-to-one**.

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QuestionDetermine whether the function is one-to-one. $f(x)=|x+4|$
Is the function one-to-one? Yes No

What is this asking? Is there only one $x$ value for every $y$ value in the function $f(x) = |x+4|$ ? Watch out! Absolute value functions can be tricky!
Remember they create "V" shapes and that can lead to the same $y$ value for different $x$ values.

1. Understand One-to-One
2. Test the Function

A one-to-one function means that for every $y$ value, there's only one $x$ value that can produce it.
Think of it like a special club where each member has a unique secret code.
No two members share the same code!

Let's pick a positive number for $f(x)$ , say $f(x) = 2$ .

$|x+4| = 2$ This means $x+4$ could equal positive 2 or negative 2.

If $x+4 = 2$ , then $x = 2 - 4 = \mathbf{-2}$ .

If $x+4 = -2$ , then $x = -2 - 4 = \mathbf{-6}$ .

Whoa! We found two different $x$ values ( $-2$ and $-6$ ) that give us the same $f(x)$ value of $2$ .
This breaks our "one $x$ for every $y$ " rule!

No, the function $f(x) = |x+4|$ is not one-to-one.