Math / Algebra

QuestionGiven $f(x)=7 x-10$ , what is the value of $f(-5)$ ? What is the value of $f(0)$ ? $\Gamma(-5)=$ $\qquad$ $f(0)=$ $\qquad$

Studdy Solution

STEP 1

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at two specific points: $x = -5$ and $x = 0$ . Watch out! Be super careful with the negative sign when plugging in $x = -5$ .
It's easy to make a mistake there!

STEP 2

1. Evaluate $f(-5)$
2. Evaluate $f(0)$

STEP 3

Alright, let's start by looking at our function: $f(x) = 7x - 10$ .
We want to find $f(-5)$ , which means we need to substitute $-5$ for $x$ everywhere we see it in the function.

STEP 4

So, let's do the substitution: $f(-5) = 7 \cdot (-5) - 10$ .
Notice how we replaced $x$ with $-5$ .

STEP 5

Now, let's calculate $7 \cdot (-5)$ , which gives us $-35$ .
So, our expression becomes $f(-5) = -35 - 10$ .

STEP 6

Finally, let's combine those two numbers. $-35 - 10$ gives us $-45$ .
Therefore, $f(-5) = -45$ .
Boom!

STEP 7

Now, let's find $f(0)$ using the same function: $f(x) = 7x - 10$ .
This time, we'll substitute $0$ for $x$ .

STEP 8

After substituting, we get $f(0) = 7 \cdot (0) - 10$ .

STEP 9

Anything multiplied by zero is zero!
So, $7 \cdot 0 = 0$ , and our expression becomes $f(0) = 0 - 10$ .

STEP 10

Finally, $0 - 10$ gives us $-10$ .
So, $f(0) = -10$ .
Fantastic!

STEP 11

We found that $f(-5) = -45$ and $f(0) = -10$ .
We're all done!

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QuestionGiven $f(x)=7 x-10$ , what is the value of $f(-5)$ ? What is the value of $f(0)$ ? $\Gamma(-5)=$ $\qquad$ $f(0)=$ $\qquad$

Studdy Solution

STEP 1

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at two specific points: $x = -5$ and $x = 0$ . Watch out! Be super careful with the negative sign when plugging in $x = -5$ .
It's easy to make a mistake there!

STEP 2

1. Evaluate $f(-5)$
2. Evaluate $f(0)$

STEP 3

Alright, let's start by looking at our function: $f(x) = 7x - 10$ .
We want to find $f(-5)$ , which means we need to substitute $-5$ for $x$ everywhere we see it in the function.

STEP 4

So, let's do the substitution: $f(-5) = 7 \cdot (-5) - 10$ .
Notice how we replaced $x$ with $-5$ .

STEP 5

Now, let's calculate $7 \cdot (-5)$ , which gives us $-35$ .
So, our expression becomes $f(-5) = -35 - 10$ .

STEP 6

Finally, let's combine those two numbers. $-35 - 10$ gives us $-45$ .
Therefore, $f(-5) = -45$ .
Boom!

STEP 7

Now, let's find $f(0)$ using the same function: $f(x) = 7x - 10$ .
This time, we'll substitute $0$ for $x$ .

STEP 8

After substituting, we get $f(0) = 7 \cdot (0) - 10$ .

STEP 9

Anything multiplied by zero is zero!
So, $7 \cdot 0 = 0$ , and our expression becomes $f(0) = 0 - 10$ .

STEP 10

Finally, $0 - 10$ gives us $-10$ .
So, $f(0) = -10$ .
Fantastic!

STEP 11

We found that $f(-5) = -45$ and $f(0) = -10$ .
We're all done!

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QuestionGiven f(x)=7x−10f(x)=7 x-10f(x)=7x−10, what is the value of f(−5)f(-5)f(−5) ? What is the value of f(0)f(0)f(0) ? Γ(−5)=\Gamma(-5)=Γ(−5)= \qquad f(0)=f(0)=f(0)= \qquad

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 two specific points: x=−5x = -5x=−5 and x=0x = 0x=0. Watch out! Be super careful with the negative sign when plugging in x=−5x = -5x=−5.It's easy to make a mistake there!

STEP 2

1. Evaluate f(−5)f(-5)f(−5)2. Evaluate f(0)f(0)f(0)

STEP 3

Alright, let's **start** by looking at our function: f(x)=7x−10f(x) = 7x - 10f(x)=7x−10.We want to find f(−5)f(-5)f(−5), which means we need to **substitute** −5-5−5 for xxx everywhere we see it in the function.

STEP 4

So, let's **do the substitution**: f(−5)=7⋅(−5)−10f(-5) = 7 \cdot (-5) - 10f(−5)=7⋅(−5)−10.Notice how we replaced xxx with −5-5−5.

STEP 5

Now, let's **calculate** 7⋅(−5)7 \cdot (-5)7⋅(−5), which gives us −35-35−35.So, our expression becomes f(−5)=−35−10f(-5) = -35 - 10f(−5)=−35−10.

STEP 6

Finally, let's **combine** those two numbers. −35−10-35 - 10−35−10 gives us −45-45−45.Therefore, f(−5)=−45f(-5) = -45f(−5)=−45.Boom!

STEP 7

Now, let's find f(0)f(0)f(0) using the same function: f(x)=7x−10f(x) = 7x - 10f(x)=7x−10.This time, we'll **substitute** 000 for xxx.

STEP 8

After **substituting**, we get f(0)=7⋅(0)−10f(0) = 7 \cdot (0) - 10f(0)=7⋅(0)−10.

STEP 9

Anything multiplied by zero is zero!So, 7⋅0=07 \cdot 0 = 07⋅0=0, and our expression becomes f(0)=0−10f(0) = 0 - 10f(0)=0−10.

STEP 10

Finally, 0−100 - 100−10 gives us −10-10−10.So, f(0)=−10f(0) = -10f(0)=−10.Fantastic!

STEP 11

We found that f(−5)=−45f(-5) = -45f(−5)=−45 and f(0)=−10f(0) = -10f(0)=−10.We're all done!

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Studdy solves anything!

Start learning now

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QuestionGiven $f(x)=7 x-10$ , what is the value of $f(-5)$ ? What is the value of $f(0)$ ? $\Gamma(-5)=$ $\qquad$ $f(0)=$ $\qquad$

What is this asking? We're given a simple function, $f(x)$ , and we need to find its value at two specific points: $x = -5$ and $x = 0$ . Watch out! Be super careful with the negative sign when plugging in $x = -5$ .
It's easy to make a mistake there!

1. Evaluate $f(-5)$
2. Evaluate $f(0)$

Alright, let's start by looking at our function: $f(x) = 7x - 10$ .
We want to find $f(-5)$ , which means we need to substitute $-5$ for $x$ everywhere we see it in the function.

So, let's do the substitution: $f(-5) = 7 \cdot (-5) - 10$ .
Notice how we replaced $x$ with $-5$ .

Now, let's calculate $7 \cdot (-5)$ , which gives us $-35$ .
So, our expression becomes $f(-5) = -35 - 10$ .

Finally, let's combine those two numbers. $-35 - 10$ gives us $-45$ .
Therefore, $f(-5) = -45$ .
Boom!

Now, let's find $f(0)$ using the same function: $f(x) = 7x - 10$ .
This time, we'll substitute $0$ for $x$ .

After substituting, we get $f(0) = 7 \cdot (0) - 10$ .

Anything multiplied by zero is zero!
So, $7 \cdot 0 = 0$ , and our expression becomes $f(0) = 0 - 10$ .

Finally, $0 - 10$ gives us $-10$ .
So, $f(0) = -10$ .
Fantastic!

We found that $f(-5) = -45$ and $f(0) = -10$ .
We're all done!