Math / Algebra

QuestionFind $f(-2)$ in this piecewise function. $\begin{array}{c} x<2, y=5 x-4 \\ x \geq 2, y=-\frac{3}{2} x+9 \\ f(-2)=[?] \end{array}$ Enter

Studdy Solution

STEP 1

What is this asking? Given two different formulas, one for $x < 2$ and another for $x \geq 2$ , what's the answer when $x = -2$ ? Watch out! Make sure to use the correct formula based on the value of $x$ !

STEP 2

1. Determine the applicable formula.
2. Calculate the result.

STEP 3

We're given a piecewise function, which means different formulas apply depending on the value of $x$ .
We need to figure out which formula to use for $x = -2$ .

STEP 4

We have two cases: $x < 2$ and $x \geq 2$ .
Since $-2$ is less than $2$ , we'll use the first formula: $y = 5x - 4$ .
It's that easy!

STEP 5

Now, substitute $x = -2$ into the chosen formula: $y = 5 \cdot (-2) - 4$ .

STEP 6

Multiply $5$ by $-2$ to get $-10$ : $y = -10 - 4$ .

STEP 7

Combine $-10$ and $-4$ by adding their magnitudes and keeping the negative sign.
So, $-10$ plus $-4$ equals $-14$ .
Therefore, $y = -14$ .
Boom!

STEP 8

$f(-2) = -14$ .

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QuestionFind $f(-2)$ in this piecewise function. $\begin{array}{c} x<2, y=5 x-4 \\ x \geq 2, y=-\frac{3}{2} x+9 \\ f(-2)=[?] \end{array}$ Enter

Studdy Solution

STEP 1

What is this asking? Given two different formulas, one for $x < 2$ and another for $x \geq 2$ , what's the answer when $x = -2$ ? Watch out! Make sure to use the correct formula based on the value of $x$ !

STEP 2

1. Determine the applicable formula.
2. Calculate the result.

STEP 3

We're given a piecewise function, which means different formulas apply depending on the value of $x$ .
We need to figure out which formula to use for $x = -2$ .

STEP 4

We have two cases: $x < 2$ and $x \geq 2$ .
Since $-2$ is less than $2$ , we'll use the first formula: $y = 5x - 4$ .
It's that easy!

STEP 5

Now, substitute $x = -2$ into the chosen formula: $y = 5 \cdot (-2) - 4$ .

STEP 6

Multiply $5$ by $-2$ to get $-10$ : $y = -10 - 4$ .

STEP 7

Combine $-10$ and $-4$ by adding their magnitudes and keeping the negative sign.
So, $-10$ plus $-4$ equals $-14$ .
Therefore, $y = -14$ .
Boom!

STEP 8

$f(-2) = -14$ .

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QuestionFind f(−2)f(-2)f(−2) in this piecewise function. x<2,y=5x−4x≥2,y=−32x+9f(−2)=[?]\begin{array}{c} x<2, y=5 x-4 \\ x \geq 2, y=-\frac{3}{2} x+9 \\ f(-2)=[?] \end{array}x<2,y=5x−4x≥2,y=−23​x+9f(−2)=[?]​ Enter

Studdy Solution

STEP 1

What is this asking? Given two different formulas, one for x<2x < 2x<2 and another for x≥2x \geq 2x≥2, what's the answer when x=−2x = -2x=−2? Watch out! Make sure to use the correct formula based on the value of xxx!

STEP 2

1. Determine the applicable formula.2. Calculate the result.

STEP 3

We're given a **piecewise function**, which means different formulas apply depending on the value of xxx.We need to figure out which formula to use for x=−2x = -2x=−2.

STEP 4

We have two cases: x<2x < 2x<2 and x≥2x \geq 2x≥2.Since −2-2−2 is less than 222, we'll use the first formula: y=5x−4y = 5x - 4y=5x−4.It's that easy!

STEP 5

Now, **substitute** x=−2x = -2x=−2 into the chosen formula: y=5⋅(−2)−4y = 5 \cdot (-2) - 4y=5⋅(−2)−4.

STEP 6

**Multiply** 555 by −2-2−2 to get −10-10−10: y=−10−4y = -10 - 4y=−10−4.

STEP 7

**Combine** −10-10−10 and −4-4−4 by adding their magnitudes and keeping the negative sign.So, −10-10−10 plus −4-4−4 equals −14-14−14.Therefore, y=−14y = -14y=−14.Boom!

STEP 8

f(−2)=−14f(-2) = -14f(−2)=−14.

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QuestionFind $f(-2)$ in this piecewise function. $\begin{array}{c} x<2, y=5 x-4 \\ x \geq 2, y=-\frac{3}{2} x+9 \\ f(-2)=[?] \end{array}$ Enter

What is this asking? Given two different formulas, one for $x < 2$ and another for $x \geq 2$ , what's the answer when $x = -2$ ? Watch out! Make sure to use the correct formula based on the value of $x$ !

1. Determine the applicable formula.
2. Calculate the result.

We're given a piecewise function, which means different formulas apply depending on the value of $x$ .
We need to figure out which formula to use for $x = -2$ .

We have two cases: $x < 2$ and $x \geq 2$ .
Since $-2$ is less than $2$ , we'll use the first formula: $y = 5x - 4$ .
It's that easy!

Now, substitute $x = -2$ into the chosen formula: $y = 5 \cdot (-2) - 4$ .

Multiply $5$ by $-2$ to get $-10$ : $y = -10 - 4$ .

Combine $-10$ and $-4$ by adding their magnitudes and keeping the negative sign.
So, $-10$ plus $-4$ equals $-14$ .
Therefore, $y = -14$ .
Boom!

$f(-2) = -14$ .