Math / Algebra

Question3) $f(x)=4 x-6$ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're given a function, $f(x) = 4x - 6$ , and we need to find the output of this function, $f(x)$ , for a bunch of different $x$ values: 0, 1, 2, 3, and 4! Watch out! Make sure to apply the correct order of operations (multiplication before subtraction) when calculating $f(x)$ !

STEP 2

1. Calculate $f(0)$
2. Calculate $f(1)$
3. Calculate $f(2)$
4. Calculate $f(3)$
5. Calculate $f(4)$

STEP 3

Let's substitute $x = 0$ into our function: $f(0) = 4 \cdot 0 - 6$ .
Remember, anything multiplied by zero is zero!

STEP 4

So, $4 \cdot 0 = 0$ , and we have $f(0) = 0 - 6 = -6$ .
Our first output is $-6$ !

STEP 5

Now, let's plug in $x = 1$ : $f(1) = 4 \cdot 1 - 6$ .

STEP 6

We get $4 \cdot 1 = 4$ , so $f(1) = 4 - 6 = -2$ .
Awesome!

STEP 7

Time for $x = 2$ : $f(2) = 4 \cdot 2 - 6$ .

STEP 8

$4 \cdot 2 = 8$ , which means $f(2) = 8 - 6 = 2$ .
Look at that positive result!

STEP 9

Let's substitute $x = 3$ : $f(3) = 4 \cdot 3 - 6$ .

STEP 10

$4 \cdot 3 = 12$ , so $f(3) = 12 - 6 = 6$ .
We're on a roll!

STEP 11

Finally, let's plug in $x = 4$ : $f(4) = 4 \cdot 4 - 6$ .

STEP 12

$4 \cdot 4 = 16$ , meaning $f(4) = 16 - 6 = 10$ .
Fantastic!

STEP 13

\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & -6 & -2 & 2 & 6 & 10 \\ \hline \end{tabular}

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Question3) $f(x)=4 x-6$ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're given a function, $f(x) = 4x - 6$ , and we need to find the output of this function, $f(x)$ , for a bunch of different $x$ values: 0, 1, 2, 3, and 4! Watch out! Make sure to apply the correct order of operations (multiplication before subtraction) when calculating $f(x)$ !

STEP 2

1. Calculate $f(0)$
2. Calculate $f(1)$
3. Calculate $f(2)$
4. Calculate $f(3)$
5. Calculate $f(4)$

STEP 3

Let's substitute $x = 0$ into our function: $f(0) = 4 \cdot 0 - 6$ .
Remember, anything multiplied by zero is zero!

STEP 4

So, $4 \cdot 0 = 0$ , and we have $f(0) = 0 - 6 = -6$ .
Our first output is $-6$ !

STEP 5

Now, let's plug in $x = 1$ : $f(1) = 4 \cdot 1 - 6$ .

STEP 6

We get $4 \cdot 1 = 4$ , so $f(1) = 4 - 6 = -2$ .
Awesome!

STEP 7

Time for $x = 2$ : $f(2) = 4 \cdot 2 - 6$ .

STEP 8

$4 \cdot 2 = 8$ , which means $f(2) = 8 - 6 = 2$ .
Look at that positive result!

STEP 9

Let's substitute $x = 3$ : $f(3) = 4 \cdot 3 - 6$ .

STEP 10

$4 \cdot 3 = 12$ , so $f(3) = 12 - 6 = 6$ .
We're on a roll!

STEP 11

Finally, let's plug in $x = 4$ : $f(4) = 4 \cdot 4 - 6$ .

STEP 12

$4 \cdot 4 = 16$ , meaning $f(4) = 16 - 6 = 10$ .
Fantastic!

STEP 13

\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & -6 & -2 & 2 & 6 & 10 \\ \hline \end{tabular}

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Question3) f(x)=4x−6f(x)=4 x-6f(x)=4x−6 \begin{tabular}{|c|c|c|c|c|c|} \hlinexxx & 0 & 1 & 2 & 3 & 4 \\ \hlinef(x)f(x)f(x) & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

STEP 2

1. Calculate f(0)f(0)f(0)2. Calculate f(1)f(1)f(1)3. Calculate f(2)f(2)f(2)4. Calculate f(3)f(3)f(3)5. Calculate f(4)f(4)f(4)

STEP 3

Let's **substitute** x=0x = 0x=0 into our function: f(0)=4⋅0−6f(0) = 4 \cdot 0 - 6f(0)=4⋅0−6.Remember, anything multiplied by **zero** is zero!

STEP 4

So, 4⋅0=04 \cdot 0 = 04⋅0=0, and we have f(0)=0−6=−6f(0) = 0 - 6 = -6f(0)=0−6=−6.Our **first output** is −6-6−6!

STEP 5

Now, let's **plug in** x=1x = 1x=1: f(1)=4⋅1−6f(1) = 4 \cdot 1 - 6f(1)=4⋅1−6.

STEP 6

We get 4⋅1=44 \cdot 1 = 44⋅1=4, so f(1)=4−6=−2f(1) = 4 - 6 = -2f(1)=4−6=−2.Awesome!

STEP 7

Time for x=2x = 2x=2: f(2)=4⋅2−6f(2) = 4 \cdot 2 - 6f(2)=4⋅2−6.

STEP 8

4⋅2=84 \cdot 2 = 84⋅2=8, which means f(2)=8−6=2f(2) = 8 - 6 = 2f(2)=8−6=2.Look at that **positive result**!

STEP 9

Let's **substitute** x=3x = 3x=3: f(3)=4⋅3−6f(3) = 4 \cdot 3 - 6f(3)=4⋅3−6.

STEP 10

4⋅3=124 \cdot 3 = 124⋅3=12, so f(3)=12−6=6f(3) = 12 - 6 = 6f(3)=12−6=6.We're on a roll!

STEP 11

Finally, let's **plug in** x=4x = 4x=4: f(4)=4⋅4−6f(4) = 4 \cdot 4 - 6f(4)=4⋅4−6.

STEP 12

4⋅4=164 \cdot 4 = 164⋅4=16, meaning f(4)=16−6=10f(4) = 16 - 6 = 10f(4)=16−6=10.Fantastic!

STEP 13

\begin{tabular}{|c|c|c|c|c|c|} \hlinexxx & 0 & 1 & 2 & 3 & 4 \\ \hlinef(x)f(x)f(x) & -6 & -2 & 2 & 6 & 10 \\ \hline \end{tabular}

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Question3) $f(x)=4 x-6$ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

1. Calculate $f(0)$
2. Calculate $f(1)$
3. Calculate $f(2)$
4. Calculate $f(3)$
5. Calculate $f(4)$

Let's substitute $x = 0$ into our function: $f(0) = 4 \cdot 0 - 6$ .
Remember, anything multiplied by zero is zero!

So, $4 \cdot 0 = 0$ , and we have $f(0) = 0 - 6 = -6$ .
Our first output is $-6$ !

Now, let's plug in $x = 1$ : $f(1) = 4 \cdot 1 - 6$ .

We get $4 \cdot 1 = 4$ , so $f(1) = 4 - 6 = -2$ .
Awesome!

Time for $x = 2$ : $f(2) = 4 \cdot 2 - 6$ .

$4 \cdot 2 = 8$ , which means $f(2) = 8 - 6 = 2$ .
Look at that positive result!

Let's substitute $x = 3$ : $f(3) = 4 \cdot 3 - 6$ .

$4 \cdot 3 = 12$ , so $f(3) = 12 - 6 = 6$ .
We're on a roll!

Finally, let's plug in $x = 4$ : $f(4) = 4 \cdot 4 - 6$ .

$4 \cdot 4 = 16$ , meaning $f(4) = 16 - 6 = 10$ .
Fantastic!

\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $f(x)$ & -6 & -2 & 2 & 6 & 10 \\ \hline \end{tabular}