QuestionGiven $f(x)=\left\{\begin{array}{ll}3 x-1 & \text { if }-3 \leq x \leq 5 \\ x^{3}-5 & \text { if } 5<x \leq 6\end{array}\right.$ , find $f(0)$ , $f(1)$ , $f(5)$ , and $f(6)$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x -1$ for $-3 \leq x \leq5$ and $x^3 -5$ for $5 < x \leq6$ . . We need to find the values of $f(x)$ for $x =0,1,5,$ and $6$ .

STEP 2

We start by finding the value of $f(0)$ . Since $0$ is within the interval $- \leq x \leq5$ , we use the first part of the piecewise function $x -1$ .
$f(0) =(0) -1$

STEP 3

Calculate the value of $f(0)$ .
$f(0) =3(0) -1 = -1$

STEP 4

Next, we find the value of $f(1)$ . Since $1$ is within the interval $-3 \leq x \leq$ , we use the first part of the piecewise function $3x -1$ .
$f(1) =3(1) -1$

STEP 5

Calculate the value of $f(1)$ .
$f(1) =3(1) -1 =2$

STEP 6

Now, we find the value of $f(5)$ . Since $5$ is within the interval $-3 \leq x \leq5$ , we use the first part of the piecewise function $3x -1$ .
$f(5) =3(5) -1$

STEP 7

Calculate the value of $f(5)$ .
$f(5) =3(5) -1 =14$

STEP 8

Finally, we find the value of $f(6)$ . Since $6$ is within the interval $5 < x \leq6$ , we use the second part of the piecewise function $x^3 -5$ .
$f(6) = (6)^3 -5$

STEP 9

Calculate the value of $f(6)$ .
$f(6) = (6)^3 -5 =211$ So, the values of the function $f(x)$ at the given points are(a) $f() = -$ (b) $f() =2$ (c) $f(5) =14$ (d) $f(6) =211$

Was this helpful?

QuestionGiven $f(x)=\left\{\begin{array}{ll}3 x-1 & \text { if }-3 \leq x \leq 5 \\ x^{3}-5 & \text { if } 5<x \leq 6\end{array}\right.$ , find $f(0)$ , $f(1)$ , $f(5)$ , and $f(6)$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x -1$ for $-3 \leq x \leq5$ and $x^3 -5$ for $5 < x \leq6$ . . We need to find the values of $f(x)$ for $x =0,1,5,$ and $6$ .

STEP 2

We start by finding the value of $f(0)$ . Since $0$ is within the interval $- \leq x \leq5$ , we use the first part of the piecewise function $x -1$ .
$f(0) =(0) -1$

STEP 3

Calculate the value of $f(0)$ .
$f(0) =3(0) -1 = -1$

STEP 4

Next, we find the value of $f(1)$ . Since $1$ is within the interval $-3 \leq x \leq$ , we use the first part of the piecewise function $3x -1$ .
$f(1) =3(1) -1$

STEP 5

Calculate the value of $f(1)$ .
$f(1) =3(1) -1 =2$

STEP 6

Now, we find the value of $f(5)$ . Since $5$ is within the interval $-3 \leq x \leq5$ , we use the first part of the piecewise function $3x -1$ .
$f(5) =3(5) -1$

STEP 7

Calculate the value of $f(5)$ .
$f(5) =3(5) -1 =14$

STEP 8

Finally, we find the value of $f(6)$ . Since $6$ is within the interval $5 < x \leq6$ , we use the second part of the piecewise function $x^3 -5$ .
$f(6) = (6)^3 -5$

STEP 9

Calculate the value of $f(6)$ .
$f(6) = (6)^3 -5 =211$ So, the values of the function $f(x)$ at the given points are(a) $f() = -$ (b) $f() =2$ (c) $f(5) =14$ (d) $f(6) =211$

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.

QuestionGiven f(x)={3x−1 if −3≤x≤5x3−5 if 5<x≤6f(x)=\left\{\begin{array}{ll}3 x-1 & \text { if }-3 \leq x \leq 5 \\ x^{3}-5 & \text { if } 5<x \leq 6\end{array}\right.f(x)={3x−1x3−5​ if −3≤x≤5 if 5<x≤6​, find f(0)f(0)f(0), f(1)f(1)f(1), f(5)f(5)f(5), and f(6)f(6)f(6).

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as a piecewise function with two parts 3x−13x -13x−1 for −3≤x≤5-3 \leq x \leq5−3≤x≤5 and x3−5x^3 -5x3−5 for 5<x≤65 < x \leq65<x≤6. . We need to find the values of f(x)f(x)f(x) for x=0,1,5,x =0,1,5,x=0,1,5, and 666.

STEP 2

We start by finding the value of f(0)f(0)f(0). Since 000 is within the interval −≤x≤5- \leq x \leq5−≤x≤5, we use the first part of the piecewise function x−1x -1x−1.f(0)=(0)−1f(0) =(0) -1f(0)=(0)−1

STEP 3

Calculate the value of f(0)f(0)f(0).f(0)=3(0)−1=−1f(0) =3(0) -1 = -1f(0)=3(0)−1=−1

STEP 4

Next, we find the value of f(1)f(1)f(1). Since 111 is within the interval −3≤x≤-3 \leq x \leq−3≤x≤, we use the first part of the piecewise function 3x−13x -13x−1.f(1)=3(1)−1f(1) =3(1) -1f(1)=3(1)−1

STEP 5

Calculate the value of f(1)f(1)f(1).f(1)=3(1)−1=2f(1) =3(1) -1 =2f(1)=3(1)−1=2

STEP 6

Now, we find the value of f(5)f(5)f(5). Since 555 is within the interval −3≤x≤5-3 \leq x \leq5−3≤x≤5, we use the first part of the piecewise function 3x−13x -13x−1.f(5)=3(5)−1f(5) =3(5) -1f(5)=3(5)−1

STEP 7

Calculate the value of f(5)f(5)f(5).f(5)=3(5)−1=14f(5) =3(5) -1 =14f(5)=3(5)−1=14

STEP 8

Finally, we find the value of f(6)f(6)f(6). Since 666 is within the interval 5<x≤65 < x \leq65<x≤6, we use the second part of the piecewise function x3−5x^3 -5x3−5.f(6)=(6)3−5f(6) = (6)^3 -5f(6)=(6)3−5

STEP 9

Calculate the value of f(6)f(6)f(6).f(6)=(6)3−5=211f(6) = (6)^3 -5 =211f(6)=(6)3−5=211So, the values of the function f(x)f(x)f(x) at the given points are(a) f()=−f() = -f()=− (b) f()=2f() =2f()=2 (c) f(5)=14f(5) =14f(5)=14 (d) f(6)=211f(6) =211f(6)=211

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.

QuestionGiven $f(x)=\left\{\begin{array}{ll}3 x-1 & \text { if }-3 \leq x \leq 5 \\ x^{3}-5 & \text { if } 5<x \leq 6\end{array}\right.$ , find $f(0)$ , $f(1)$ , $f(5)$ , and $f(6)$ .

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x -1$ for $-3 \leq x \leq5$ and $x^3 -5$ for $5 < x \leq6$ . . We need to find the values of $f(x)$ for $x =0,1,5,$ and $6$ .

We start by finding the value of $f(0)$ . Since $0$ is within the interval $- \leq x \leq5$ , we use the first part of the piecewise function $x -1$ .
$f(0) =(0) -1$

Calculate the value of $f(0)$ .
$f(0) =3(0) -1 = -1$

Next, we find the value of $f(1)$ . Since $1$ is within the interval $-3 \leq x \leq$ , we use the first part of the piecewise function $3x -1$ .
$f(1) =3(1) -1$

Calculate the value of $f(1)$ .
$f(1) =3(1) -1 =2$

Now, we find the value of $f(5)$ . Since $5$ is within the interval $-3 \leq x \leq5$ , we use the first part of the piecewise function $3x -1$ .
$f(5) =3(5) -1$

Calculate the value of $f(5)$ .
$f(5) =3(5) -1 =14$

Finally, we find the value of $f(6)$ . Since $6$ is within the interval $5 < x \leq6$ , we use the second part of the piecewise function $x^3 -5$ .
$f(6) = (6)^3 -5$

Calculate the value of $f(6)$ .
$f(6) = (6)^3 -5 =211$ So, the values of the function $f(x)$ at the given points are(a) $f() = -$ (b) $f() =2$ (c) $f(5) =14$ (d) $f(6) =211$