Math / Algebra

QuestionFind $f(1)$ in this piecewise function. $\begin{array}{c} x<2, y=-2 x+10 \\ x \geq 2, y=\frac{3}{2} x+3 \\ f(1)=[?] \end{array}$ Enter

Studdy Solution

STEP 1

What is this asking? We need to find the value of a piecewise function $f(x)$ when $x = 1$ . Watch out! Make sure to plug the $x$ value into the correct piece of the function!

STEP 2

1. Determine the relevant piece
2. Evaluate the function

STEP 3

Alright, so we've got this funky piecewise function, and we want to find $f(1)$ .
Piecewise functions are like a choose-your-own-adventure for math!
We need to figure out which piece of the function to use based on the value of $x$ .

STEP 4

We're looking for $f(1)$ , so our $x$ value is $1$ .
Let's look at the conditions for each piece.
The first piece is used when $x < 2$ , and the second piece is used when $x \geq 2$ .

STEP 5

Since our $x$ value is $1$ , and $1 < 2$ , we're definitely using the first piece of the function: $y = -2x + 10$ .
Woohoo! We've chosen our adventure path!

STEP 6

Now, we just need to plug in our $x$ value, which is $\textbf{1}$ , into the correct piece of the function, which we found to be $y = -2x + 10$ .

STEP 7

Let's substitute $x = 1$ into the equation: $y = -2 \cdot (\textbf{1}) + 10$

STEP 8

Multiply $-2$ by $1$ : $y = -2 + 10$

STEP 9

Add $-2$ to $10$ : $y = 8$

STEP 10

So, $f(1) = \textbf{8}$ !
We did it!

STEP 11

$f(1) = 8$

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QuestionFind $f(1)$ in this piecewise function. $\begin{array}{c} x<2, y=-2 x+10 \\ x \geq 2, y=\frac{3}{2} x+3 \\ f(1)=[?] \end{array}$ Enter

Studdy Solution

STEP 1

What is this asking? We need to find the value of a piecewise function $f(x)$ when $x = 1$ . Watch out! Make sure to plug the $x$ value into the correct piece of the function!

STEP 2

1. Determine the relevant piece
2. Evaluate the function

STEP 3

Alright, so we've got this funky piecewise function, and we want to find $f(1)$ .
Piecewise functions are like a choose-your-own-adventure for math!
We need to figure out which piece of the function to use based on the value of $x$ .

STEP 4

We're looking for $f(1)$ , so our $x$ value is $1$ .
Let's look at the conditions for each piece.
The first piece is used when $x < 2$ , and the second piece is used when $x \geq 2$ .

STEP 5

Since our $x$ value is $1$ , and $1 < 2$ , we're definitely using the first piece of the function: $y = -2x + 10$ .
Woohoo! We've chosen our adventure path!

STEP 6

Now, we just need to plug in our $x$ value, which is $\textbf{1}$ , into the correct piece of the function, which we found to be $y = -2x + 10$ .

STEP 7

Let's substitute $x = 1$ into the equation: $y = -2 \cdot (\textbf{1}) + 10$

STEP 8

Multiply $-2$ by $1$ : $y = -2 + 10$

STEP 9

Add $-2$ to $10$ : $y = 8$

STEP 10

So, $f(1) = \textbf{8}$ !
We did it!

STEP 11

$f(1) = 8$

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QuestionFind f(1)f(1)f(1) in this piecewise function. x<2,y=−2x+10x≥2,y=32x+3f(1)=[?]\begin{array}{c} x<2, y=-2 x+10 \\ x \geq 2, y=\frac{3}{2} x+3 \\ f(1)=[?] \end{array}x<2,y=−2x+10x≥2,y=23​x+3f(1)=[?]​ Enter

Studdy Solution

STEP 1

What is this asking? We need to find the value of a piecewise function f(x)f(x)f(x) when x=1x = 1x=1. Watch out! Make sure to plug the xxx value into the correct piece of the function!

STEP 2

1. Determine the relevant piece2. Evaluate the function

STEP 3

Alright, so we've got this *funky* piecewise function, and we want to find f(1)f(1)f(1).Piecewise functions are like a choose-your-own-adventure for math!We need to figure out which piece of the function to use based on the value of xxx.

STEP 4

We're looking for f(1)f(1)f(1), so our xxx value is 111.Let's look at the conditions for each piece.The first piece is used when x<2x < 2x<2, and the second piece is used when x≥2x \geq 2x≥2.

STEP 5

Since our xxx value is 111, and 1<21 < 21<2, we're definitely using the first piece of the function: y=−2x+10y = -2x + 10y=−2x+10.Woohoo! We've chosen our adventure path!

STEP 6

Now, we just need to plug in our xxx value, which is 1\textbf{1}1, into the correct piece of the function, which we found to be y=−2x+10y = -2x + 10y=−2x+10.

STEP 7

Let's **substitute** x=1x = 1x=1 into the equation: y=−2⋅(1)+10y = -2 \cdot (\textbf{1}) + 10y=−2⋅(1)+10

STEP 8

**Multiply** −2-2−2 by 111: y=−2+10y = -2 + 10y=−2+10

STEP 9

**Add** −2-2−2 to 101010: y=8y = 8y=8

STEP 10

So, f(1)=8f(1) = \textbf{8}f(1)=8!We did it!

STEP 11

f(1)=8f(1) = 8f(1)=8

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Studdy solves anything!

Start learning now

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QuestionFind $f(1)$ in this piecewise function. $\begin{array}{c} x<2, y=-2 x+10 \\ x \geq 2, y=\frac{3}{2} x+3 \\ f(1)=[?] \end{array}$ Enter

What is this asking? We need to find the value of a piecewise function $f(x)$ when $x = 1$ . Watch out! Make sure to plug the $x$ value into the correct piece of the function!

1. Determine the relevant piece
2. Evaluate the function

Alright, so we've got this funky piecewise function, and we want to find $f(1)$ .
Piecewise functions are like a choose-your-own-adventure for math!
We need to figure out which piece of the function to use based on the value of $x$ .

We're looking for $f(1)$ , so our $x$ value is $1$ .
Let's look at the conditions for each piece.
The first piece is used when $x < 2$ , and the second piece is used when $x \geq 2$ .

Since our $x$ value is $1$ , and $1 < 2$ , we're definitely using the first piece of the function: $y = -2x + 10$ .
Woohoo! We've chosen our adventure path!

Now, we just need to plug in our $x$ value, which is $\textbf{1}$ , into the correct piece of the function, which we found to be $y = -2x + 10$ .

Let's substitute $x = 1$ into the equation: $y = -2 \cdot (\textbf{1}) + 10$

Multiply $-2$ by $1$ : $y = -2 + 10$

Add $-2$ to $10$ : $y = 8$

So, $f(1) = \textbf{8}$ !
We did it!

$f(1) = 8$