QuestionFind (a) $f(-1)$ , (b) $f(0)$ , and (c) $f(4)$ for the piecewise function $f(x)$ defined as: $f(x)=\left\{\begin{array}{ll} x^{2} & \text { if } x<0 \\ 0 & \text { if } x=0 \\ 3 x+3 & \text { if } x>0 \end{array}\right.$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions for different ranges of $x$ . . We need to find the values of $f(x)$ for $x=-1$ , $x=0$ , and $x=4$ .

STEP 2

We start by finding $f(-1)$ . Since $-1$ is less than $0$ , we use the expression $x^{2}$ .
$f(-1) = (-1)^{2}$

STEP 3

Calculate the value of $f(-1)$ .
$f(-1) = (-1)^{2} =1$

STEP 4

Next, we find $f(0)$ . Since $0$ is equal to $0$ , we use the expression $0$ .
$f(0) =0$

STEP 5

Calculate the value of $f(0)$ .
$f(0) =0$

STEP 6

Finally, we find $f(4)$ . Since $4$ is greater than $0$ , we use the expression $3x+3$ .
$f(4) =3(4) +3$

STEP 7

Calculate the value of $f(4)$ .
$f(4) =3(4) +3 =15$ So, $f(-1) =1$ , $f(0) =0$ , and $f(4) =15$ .

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QuestionFind (a) $f(-1)$ , (b) $f(0)$ , and (c) $f(4)$ for the piecewise function $f(x)$ defined as: $f(x)=\left\{\begin{array}{ll} x^{2} & \text { if } x<0 \\ 0 & \text { if } x=0 \\ 3 x+3 & \text { if } x>0 \end{array}\right.$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions for different ranges of $x$ . . We need to find the values of $f(x)$ for $x=-1$ , $x=0$ , and $x=4$ .

STEP 2

We start by finding $f(-1)$ . Since $-1$ is less than $0$ , we use the expression $x^{2}$ .
$f(-1) = (-1)^{2}$

STEP 3

Calculate the value of $f(-1)$ .
$f(-1) = (-1)^{2} =1$

STEP 4

Next, we find $f(0)$ . Since $0$ is equal to $0$ , we use the expression $0$ .
$f(0) =0$

STEP 5

Calculate the value of $f(0)$ .
$f(0) =0$

STEP 6

Finally, we find $f(4)$ . Since $4$ is greater than $0$ , we use the expression $3x+3$ .
$f(4) =3(4) +3$

STEP 7

Calculate the value of $f(4)$ .
$f(4) =3(4) +3 =15$ So, $f(-1) =1$ , $f(0) =0$ , and $f(4) =15$ .

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Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as a piecewise function with three different expressions for different ranges of xxx. . We need to find the values of f(x)f(x)f(x) for x=−1x=-1x=−1, x=0x=0x=0, and x=4x=4x=4.

STEP 2

We start by finding f(−1)f(-1)f(−1). Since −1-1−1 is less than 000, we use the expression x2x^{2}x2.f(−1)=(−1)2f(-1) = (-1)^{2}f(−1)=(−1)2

STEP 3

Calculate the value of f(−1)f(-1)f(−1).f(−1)=(−1)2=1f(-1) = (-1)^{2} =1f(−1)=(−1)2=1

STEP 4

Next, we find f(0)f(0)f(0). Since 000 is equal to 000, we use the expression 000.f(0)=0f(0) =0f(0)=0

STEP 5

Calculate the value of f(0)f(0)f(0).f(0)=0f(0) =0f(0)=0

STEP 6

Finally, we find f(4)f(4)f(4). Since 444 is greater than 000, we use the expression 3x+33x+33x+3.f(4)=3(4)+3f(4) =3(4) +3f(4)=3(4)+3

STEP 7

Calculate the value of f(4)f(4)f(4).f(4)=3(4)+3=15f(4) =3(4) +3 =15f(4)=3(4)+3=15So, f(−1)=1f(-1) =1f(−1)=1, f(0)=0f(0) =0f(0)=0, and f(4)=15f(4) =15f(4)=15.

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Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions for different ranges of $x$ . . We need to find the values of $f(x)$ for $x=-1$ , $x=0$ , and $x=4$ .

We start by finding $f(-1)$ . Since $-1$ is less than $0$ , we use the expression $x^{2}$ .
$f(-1) = (-1)^{2}$

Calculate the value of $f(-1)$ .
$f(-1) = (-1)^{2} =1$

Next, we find $f(0)$ . Since $0$ is equal to $0$ , we use the expression $0$ .
$f(0) =0$

Calculate the value of $f(0)$ .
$f(0) =0$

Finally, we find $f(4)$ . Since $4$ is greater than $0$ , we use the expression $3x+3$ .
$f(4) =3(4) +3$

Calculate the value of $f(4)$ .
$f(4) =3(4) +3 =15$ So, $f(-1) =1$ , $f(0) =0$ , and $f(4) =15$ .