Math / Algebra

QuestionGiven the following functions, find the indicated values. $f(x)=8-6 x$ (a) $f(-7)$ (b) $f(0)$ (c) $f(8)$ (a) $f(-7)=$

Studdy Solution

STEP 1

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at three different inputs: $x = -7$ , $x = 0$ , and $x = 8$ . Watch out! Be super careful with the signs when substituting negative values!
It's easy to make a mistake there.

STEP 2

1. Evaluate $f(-7)$
2. Evaluate $f(0)$
3. Evaluate $f(8)$

STEP 3

Alright, let's kick things off with $f(-7)$ !
We're given the function $f(x) = 8 - 6x$ .
So, to find $f(-7)$ , we need to substitute $-7$ for $x$ in the function.

STEP 4

Let's do it!
We have $f(-7) = 8 - 6 \cdot (-7)$ .
Notice how we're multiplying $-6$ by $-7$ .

STEP 5

Now, a negative times a negative is a positive, so $-6 \cdot (-7)$ becomes $+42$ .
So, we have $f(-7) = 8 + 42$ .

STEP 6

Adding those together, we get $f(-7) = 50$ .
Awesome!

STEP 7

Next up, let's find $f(0)$ .
Again, we substitute $0$ for $x$ in our function $f(x) = 8 - 6x$ .

STEP 8

This gives us $f(0) = 8 - 6 \cdot 0$ .

STEP 9

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Therefore, $f(0) = 8 - 0 = 8$ .
Nice and clean!

STEP 10

Finally, let's tackle $f(8)$ .
We substitute $8$ for $x$ in $f(x) = 8 - 6x$ .

STEP 11

This gives us $f(8) = 8 - 6 \cdot 8$ .

STEP 12

Now, $6 \cdot 8 = 48$ , so we have $f(8) = 8 - 48$ .

STEP 13

Subtracting gives us $f(8) = -40$ .
Fantastic!

STEP 14

We found that $f(-7) = 50$ , $f(0) = 8$ , and $f(8) = -40$ .
We rocked it!

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QuestionGiven the following functions, find the indicated values. $f(x)=8-6 x$ (a) $f(-7)$ (b) $f(0)$ (c) $f(8)$ (a) $f(-7)=$

Studdy Solution

STEP 1

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at three different inputs: $x = -7$ , $x = 0$ , and $x = 8$ . Watch out! Be super careful with the signs when substituting negative values!
It's easy to make a mistake there.

STEP 2

1. Evaluate $f(-7)$
2. Evaluate $f(0)$
3. Evaluate $f(8)$

STEP 3

Alright, let's kick things off with $f(-7)$ !
We're given the function $f(x) = 8 - 6x$ .
So, to find $f(-7)$ , we need to substitute $-7$ for $x$ in the function.

STEP 4

Let's do it!
We have $f(-7) = 8 - 6 \cdot (-7)$ .
Notice how we're multiplying $-6$ by $-7$ .

STEP 5

Now, a negative times a negative is a positive, so $-6 \cdot (-7)$ becomes $+42$ .
So, we have $f(-7) = 8 + 42$ .

STEP 6

Adding those together, we get $f(-7) = 50$ .
Awesome!

STEP 7

Next up, let's find $f(0)$ .
Again, we substitute $0$ for $x$ in our function $f(x) = 8 - 6x$ .

STEP 8

This gives us $f(0) = 8 - 6 \cdot 0$ .

STEP 9

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Therefore, $f(0) = 8 - 0 = 8$ .
Nice and clean!

STEP 10

Finally, let's tackle $f(8)$ .
We substitute $8$ for $x$ in $f(x) = 8 - 6x$ .

STEP 11

This gives us $f(8) = 8 - 6 \cdot 8$ .

STEP 12

Now, $6 \cdot 8 = 48$ , so we have $f(8) = 8 - 48$ .

STEP 13

Subtracting gives us $f(8) = -40$ .
Fantastic!

STEP 14

We found that $f(-7) = 50$ , $f(0) = 8$ , and $f(8) = -40$ .
We rocked it!

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QuestionGiven the following functions, find the indicated values. f(x)=8−6xf(x)=8-6 xf(x)=8−6x (a) f(−7)f(-7)f(−7) (b) f(0)f(0)f(0) (c) f(8)f(8)f(8) (a) f(−7)=f(-7)=f(−7)=

Studdy Solution

STEP 1

What is this asking? We're given a simple function, f(x)f(x)f(x), and we need to find its value at three different inputs: x=−7x = -7x=−7, x=0x = 0x=0, and x=8x = 8x=8. Watch out! Be super careful with the signs when substituting negative values!It's easy to make a mistake there.

STEP 2

1. Evaluate f(−7)f(-7)f(−7)2. Evaluate f(0)f(0)f(0)3. Evaluate f(8)f(8)f(8)

STEP 3

Alright, let's **kick things off** with f(−7)f(-7)f(−7)!We're given the function f(x)=8−6xf(x) = 8 - 6xf(x)=8−6x.So, to find f(−7)f(-7)f(−7), we need to **substitute** −7-7−7 for xxx in the function.

STEP 4

Let's do it!We have f(−7)=8−6⋅(−7)f(-7) = 8 - 6 \cdot (-7)f(−7)=8−6⋅(−7).Notice how we're **multiplying** −6-6−6 by −7-7−7.

STEP 5

Now, a negative times a negative is a positive, so −6⋅(−7)-6 \cdot (-7)−6⋅(−7) becomes +42+42+42.So, we have f(−7)=8+42f(-7) = 8 + 42f(−7)=8+42.

STEP 6

Adding those together, we get f(−7)=50f(-7) = 50f(−7)=50.Awesome!

STEP 7

Next up, let's find f(0)f(0)f(0).Again, we **substitute** 000 for xxx in our function f(x)=8−6xf(x) = 8 - 6xf(x)=8−6x.

STEP 8

This gives us f(0)=8−6⋅0f(0) = 8 - 6 \cdot 0f(0)=8−6⋅0.

STEP 9

Anything multiplied by zero is zero, so 6⋅0=06 \cdot 0 = 06⋅0=0.Therefore, f(0)=8−0=8f(0) = 8 - 0 = 8f(0)=8−0=8.Nice and clean!

STEP 10

Finally, let's **tackle** f(8)f(8)f(8).We **substitute** 888 for xxx in f(x)=8−6xf(x) = 8 - 6xf(x)=8−6x.

STEP 11

This gives us f(8)=8−6⋅8f(8) = 8 - 6 \cdot 8f(8)=8−6⋅8.

STEP 12

Now, 6⋅8=486 \cdot 8 = 486⋅8=48, so we have f(8)=8−48f(8) = 8 - 48f(8)=8−48.

STEP 13

Subtracting gives us f(8)=−40f(8) = -40f(8)=−40.Fantastic!

STEP 14

We found that f(−7)=50f(-7) = 50f(−7)=50, f(0)=8f(0) = 8f(0)=8, and f(8)=−40f(8) = -40f(8)=−40.We rocked it!

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QuestionGiven the following functions, find the indicated values. $f(x)=8-6 x$ (a) $f(-7)$ (b) $f(0)$ (c) $f(8)$ (a) $f(-7)=$

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at three different inputs: $x = -7$ , $x = 0$ , and $x = 8$ . Watch out! Be super careful with the signs when substituting negative values!
It's easy to make a mistake there.

1. Evaluate $f(-7)$
2. Evaluate $f(0)$
3. Evaluate $f(8)$

Alright, let's kick things off with $f(-7)$ !
We're given the function $f(x) = 8 - 6x$ .
So, to find $f(-7)$ , we need to substitute $-7$ for $x$ in the function.

Let's do it!
We have $f(-7) = 8 - 6 \cdot (-7)$ .
Notice how we're multiplying $-6$ by $-7$ .

Now, a negative times a negative is a positive, so $-6 \cdot (-7)$ becomes $+42$ .
So, we have $f(-7) = 8 + 42$ .

Adding those together, we get $f(-7) = 50$ .
Awesome!

Next up, let's find $f(0)$ .
Again, we substitute $0$ for $x$ in our function $f(x) = 8 - 6x$ .

This gives us $f(0) = 8 - 6 \cdot 0$ .

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Therefore, $f(0) = 8 - 0 = 8$ .
Nice and clean!

Finally, let's tackle $f(8)$ .
We substitute $8$ for $x$ in $f(x) = 8 - 6x$ .

This gives us $f(8) = 8 - 6 \cdot 8$ .

Now, $6 \cdot 8 = 48$ , so we have $f(8) = 8 - 48$ .

Subtracting gives us $f(8) = -40$ .
Fantastic!

We found that $f(-7) = 50$ , $f(0) = 8$ , and $f(8) = -40$ .
We rocked it!