Math / Algebra

Question6. 1. Evaluate the following for $f(x)=\left\{\begin{array}{cc}3 x-5, & x \geq 2 \\ x^{2}, & x<2\end{array}\right.$ a) $f(-5)$ b) $f(2)$ c) $f(5)$

Studdy Solution

STEP 1

What is this asking? We're given a piecewise function $f(x)$ , which means it acts differently depending on the input $x$ , and we need to find its value at three different $x$ values: $-5$ , $2$ , and $5$ . Watch out! Make sure to plug each $x$ value into the correct piece of the function!
The conditions tell you which formula to use.

STEP 2

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

STEP 3

Alright, let's start with $f(-5)$ !
Since $-5$ is less than $2$ , we'll use the second formula: $f(x) = x^2$ .

STEP 4

Substitute $-5$ for $x$ : $f(-5) = (-5)^2$

STEP 5

Calculate the square: $f(-5) = (-5) \cdot (-5) = 25$ So, $f(-5) = \textbf{25}$ !

STEP 6

Next up, $f(2)$ !
Since $2$ is greater than or equal to $2$ , we use the first formula: $f(x) = 3x - 5$ .

STEP 7

Substitute $2$ for $x$ : $f(2) = 3 \cdot (2) - 5$

STEP 8

Multiply, then subtract: $f(2) = 6 - 5 = 1$ So, $f(2) = \textbf{1}$ !

STEP 9

Finally, let's find $f(5)$ !
Since $5$ is greater than $2$ , we use the first formula again: $f(x) = 3x - 5$ .

STEP 10

Substitute $5$ for $x$ : $f(5) = 3 \cdot (5) - 5$

STEP 11

Multiply, then subtract: $f(5) = 15 - 5 = 10$ Therefore, $f(5) = \textbf{10}$ !

STEP 12

$f(-5) = 25$ , $f(2) = 1$ , and $f(5) = 10$ .
We've conquered the piecewise function!

Was this helpful?

Question6. 1. Evaluate the following for $f(x)=\left\{\begin{array}{cc}3 x-5, & x \geq 2 \\ x^{2}, & x<2\end{array}\right.$ a) $f(-5)$ b) $f(2)$ c) $f(5)$

Studdy Solution

STEP 1

STEP 2

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

STEP 3

Alright, let's start with $f(-5)$ !
Since $-5$ is less than $2$ , we'll use the second formula: $f(x) = x^2$ .

STEP 4

Substitute $-5$ for $x$ : $f(-5) = (-5)^2$

STEP 5

Calculate the square: $f(-5) = (-5) \cdot (-5) = 25$ So, $f(-5) = \textbf{25}$ !

STEP 6

Next up, $f(2)$ !
Since $2$ is greater than or equal to $2$ , we use the first formula: $f(x) = 3x - 5$ .

STEP 7

Substitute $2$ for $x$ : $f(2) = 3 \cdot (2) - 5$

STEP 8

Multiply, then subtract: $f(2) = 6 - 5 = 1$ So, $f(2) = \textbf{1}$ !

STEP 9

Finally, let's find $f(5)$ !
Since $5$ is greater than $2$ , we use the first formula again: $f(x) = 3x - 5$ .

STEP 10

Substitute $5$ for $x$ : $f(5) = 3 \cdot (5) - 5$

STEP 11

Multiply, then subtract: $f(5) = 15 - 5 = 10$ Therefore, $f(5) = \textbf{10}$ !

STEP 12

$f(-5) = 25$ , $f(2) = 1$ , and $f(5) = 10$ .
We've conquered the piecewise function!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question6. 1. Evaluate the following for f(x)={3x−5,x≥2x2,x<2f(x)=\left\{\begin{array}{cc}3 x-5, & x \geq 2 \\ x^{2}, & x<2\end{array}\right.f(x)={3x−5,x2,​x≥2x<2​ a) f(−5)f(-5)f(−5) b) f(2)f(2)f(2) c) f(5)f(5)f(5)

Studdy Solution

STEP 1

STEP 2

1. Evaluate f(−5)f(-5)f(−5)2. Evaluate f(2)f(2)f(2)3. Evaluate f(5)f(5)f(5)

STEP 3

Alright, let's **start** with f(−5)f(-5)f(−5)!Since −5-5−5 is *less than* 222, we'll use the second formula: f(x)=x2f(x) = x^2f(x)=x2.

STEP 4

**Substitute** −5-5−5 for xxx: f(−5)=(−5)2f(-5) = (-5)^2f(−5)=(−5)2

STEP 5

**Calculate** the square: f(−5)=(−5)⋅(−5)=25f(-5) = (-5) \cdot (-5) = 25f(−5)=(−5)⋅(−5)=25 So, f(−5)=25f(-5) = \textbf{25}f(−5)=25!

STEP 6

Next up, f(2)f(2)f(2)!Since 222 is *greater than or equal to* 222, we use the *first* formula: f(x)=3x−5f(x) = 3x - 5f(x)=3x−5.

STEP 7

**Substitute** 222 for xxx: f(2)=3⋅(2)−5f(2) = 3 \cdot (2) - 5f(2)=3⋅(2)−5

STEP 8

**Multiply**, then **subtract**: f(2)=6−5=1f(2) = 6 - 5 = 1f(2)=6−5=1 So, f(2)=1f(2) = \textbf{1}f(2)=1!

STEP 9

Finally, let's find f(5)f(5)f(5)!Since 555 is *greater than* 222, we use the *first* formula *again*: f(x)=3x−5f(x) = 3x - 5f(x)=3x−5.

STEP 10

**Substitute** 555 for xxx: f(5)=3⋅(5)−5f(5) = 3 \cdot (5) - 5f(5)=3⋅(5)−5

STEP 11

**Multiply**, then **subtract**: f(5)=15−5=10f(5) = 15 - 5 = 10f(5)=15−5=10 Therefore, f(5)=10f(5) = \textbf{10}f(5)=10!

STEP 12

f(−5)=25f(-5) = 25f(−5)=25, f(2)=1f(2) = 1f(2)=1, and f(5)=10f(5) = 10f(5)=10.We've conquered the piecewise function!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question6. 1. Evaluate the following for $f(x)=\left\{\begin{array}{cc}3 x-5, & x \geq 2 \\ x^{2}, & x<2\end{array}\right.$ a) $f(-5)$ b) $f(2)$ c) $f(5)$

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

Alright, let's start with $f(-5)$ !
Since $-5$ is less than $2$ , we'll use the second formula: $f(x) = x^2$ .

Substitute $-5$ for $x$ : $f(-5) = (-5)^2$

Calculate the square: $f(-5) = (-5) \cdot (-5) = 25$ So, $f(-5) = \textbf{25}$ !

Next up, $f(2)$ !
Since $2$ is greater than or equal to $2$ , we use the first formula: $f(x) = 3x - 5$ .

Substitute $2$ for $x$ : $f(2) = 3 \cdot (2) - 5$

Multiply, then subtract: $f(2) = 6 - 5 = 1$ So, $f(2) = \textbf{1}$ !

Finally, let's find $f(5)$ !
Since $5$ is greater than $2$ , we use the first formula again: $f(x) = 3x - 5$ .

Substitute $5$ for $x$ : $f(5) = 3 \cdot (5) - 5$

Multiply, then subtract: $f(5) = 15 - 5 = 10$ Therefore, $f(5) = \textbf{10}$ !

$f(-5) = 25$ , $f(2) = 1$ , and $f(5) = 10$ .
We've conquered the piecewise function!