QuestionEvaluate the piecewise function $f(x)=\left\{\begin{array}{lll}3 x+5 & \text { if } & x<0 \\ 4 x+7 & \text { if } & x \geq 0\end{array}\right.$ for $f(-2)$ , $f(0)$ , and $f(3)$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x+5$ if $x<0$ , and $4x+7$ if $x \geq0$ .

STEP 2

We need to evaluate the function $f(x)$ at three different values $-2$ , $0$ , and $$.
a. To find $f(-2)$ , we need to determine which part of the piecewise function to use. Since $-2$ is less than $0$ , we use the first part of the function $x+5$ .
$f(-2) =(-2) +5$

STEP 3

Now, calculate the value of $f(-2)$ .
$f(-2) =3(-2) +5 = -6 +5 = -1$

STEP 4

b. To find $f(0)$ , we need to determine which part of the piecewise function to use. Since $0$ is equal to $0$ , we use the second part of the function $4x+7$ .
$f(0) =4(0) +7$

STEP 5

Now, calculate the value of $f(0)$ .
$f(0) =4(0) +7 =0 +7 =7$

STEP 6

c. To find $f(3)$ , we need to determine which part of the piecewise function to use. Since $3$ is greater than $0$ , we use the second part of the function $4x+$ .
$f(3) =4(3) +$

STEP 7

Now, calculate the value of $f(3)$ .
$f(3) =4(3) +7 =12 +7 =19$ So, $f(-2) = -1$ , $f(0) =7$ , and $f(3) =19$ .

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QuestionEvaluate the piecewise function $f(x)=\left\{\begin{array}{lll}3 x+5 & \text { if } & x<0 \\ 4 x+7 & \text { if } & x \geq 0\end{array}\right.$ for $f(-2)$ , $f(0)$ , and $f(3)$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x+5$ if $x<0$ , and $4x+7$ if $x \geq0$ .

STEP 2

We need to evaluate the function $f(x)$ at three different values $-2$ , $0$ , and $$.
a. To find $f(-2)$ , we need to determine which part of the piecewise function to use. Since $-2$ is less than $0$ , we use the first part of the function $x+5$ .
$f(-2) =(-2) +5$

STEP 3

Now, calculate the value of $f(-2)$ .
$f(-2) =3(-2) +5 = -6 +5 = -1$

STEP 4

b. To find $f(0)$ , we need to determine which part of the piecewise function to use. Since $0$ is equal to $0$ , we use the second part of the function $4x+7$ .
$f(0) =4(0) +7$

STEP 5

Now, calculate the value of $f(0)$ .
$f(0) =4(0) +7 =0 +7 =7$

STEP 6

c. To find $f(3)$ , we need to determine which part of the piecewise function to use. Since $3$ is greater than $0$ , we use the second part of the function $4x+$ .
$f(3) =4(3) +$

STEP 7

Now, calculate the value of $f(3)$ .
$f(3) =4(3) +7 =12 +7 =19$ So, $f(-2) = -1$ , $f(0) =7$ , and $f(3) =19$ .

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QuestionEvaluate the piecewise function f(x)={3x+5 if x<04x+7 if x≥0f(x)=\left\{\begin{array}{lll}3 x+5 & \text { if } & x<0 \\ 4 x+7 & \text { if } & x \geq 0\end{array}\right.f(x)={3x+54x+7​ if if ​x<0x≥0​ for f(−2)f(-2)f(−2), f(0)f(0)f(0), and f(3)f(3)f(3).

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as a piecewise function with two parts 3x+53x+53x+5 if x<0x<0x<0, and 4x+74x+74x+7 if x≥0x \geq0x≥0.

STEP 2

STEP 3

Now, calculate the value of f(−2)f(-2)f(−2).f(−2)=3(−2)+5=−6+5=−1f(-2) =3(-2) +5 = -6 +5 = -1f(−2)=3(−2)+5=−6+5=−1

STEP 4

b. To find f(0)f(0)f(0), we need to determine which part of the piecewise function to use. Since 000 is equal to 000, we use the second part of the function 4x+74x+74x+7.f(0)=4(0)+7f(0) =4(0) +7f(0)=4(0)+7

STEP 5

Now, calculate the value of f(0)f(0)f(0).f(0)=4(0)+7=0+7=7f(0) =4(0) +7 =0 +7 =7f(0)=4(0)+7=0+7=7

STEP 6

c. To find f(3)f(3)f(3), we need to determine which part of the piecewise function to use. Since 333 is greater than 000, we use the second part of the function 4x+4x+4x+.f(3)=4(3)+f(3) =4(3) +f(3)=4(3)+

STEP 7

Now, calculate the value of f(3)f(3)f(3).f(3)=4(3)+7=12+7=19f(3) =4(3) +7 =12 +7 =19f(3)=4(3)+7=12+7=19So, f(−2)=−1f(-2) = -1f(−2)=−1, f(0)=7f(0) =7f(0)=7, and f(3)=19f(3) =19f(3)=19.

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QuestionEvaluate the piecewise function $f(x)=\left\{\begin{array}{lll}3 x+5 & \text { if } & x<0 \\ 4 x+7 & \text { if } & x \geq 0\end{array}\right.$ for $f(-2)$ , $f(0)$ , and $f(3)$ .

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts $3x+5$ if $x<0$ , and $4x+7$ if $x \geq0$ .

Now, calculate the value of $f(-2)$ .
$f(-2) =3(-2) +5 = -6 +5 = -1$

b. To find $f(0)$ , we need to determine which part of the piecewise function to use. Since $0$ is equal to $0$ , we use the second part of the function $4x+7$ .
$f(0) =4(0) +7$

Now, calculate the value of $f(0)$ .
$f(0) =4(0) +7 =0 +7 =7$

c. To find $f(3)$ , we need to determine which part of the piecewise function to use. Since $3$ is greater than $0$ , we use the second part of the function $4x+$ .
$f(3) =4(3) +$

Now, calculate the value of $f(3)$ .
$f(3) =4(3) +7 =12 +7 =19$ So, $f(-2) = -1$ , $f(0) =7$ , and $f(3) =19$ .