Solved on Jan 19, 2024

Evaluate the piecewise function $g(x)$ at different values in its domain: $g(-4), g(-2), g(0), g(3), g(4)$ .

STEP 1

Assumptions
1. The function $g(x)$ is defined piecewise with two different expressions: - $x+4$ for $-5 \leq x \leq -1$ - $2-x$ for $-1 < x \leq 5$
2. We need to evaluate $g(x)$ at specific values: $-4, -2, 0, 3, 4$ .

STEP 2

To evaluate $g(-4)$ , we need to determine which piece of the piecewise function to use. Since $-4$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-4) = (-4) + 4$

STEP 3

Calculate the value of $g(-4)$ .
$g(-4) = -4 + 4 = 0$

STEP 4

To evaluate $g(-2)$ , we again determine which piece of the piecewise function to use. Since $-2$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-2) = (-2) + 4$

STEP 5

Calculate the value of $g(-2)$ .
$g(-2) = -2 + 4 = 2$

STEP 6

To evaluate $g(0)$ , we need to determine which piece of the piecewise function to use. Since $0$ is in the interval $(-1, 5]$ , we use the second expression.
$g(0) = 2 - (0)$

STEP 7

Calculate the value of $g(0)$ .
$g(0) = 2 - 0 = 2$

STEP 8

To evaluate $g(3)$ , we determine which piece of the piecewise function to use. Since $3$ is in the interval $(-1, 5]$ , we use the second expression.
$g(3) = 2 - (3)$

STEP 9

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

STEP 10

To evaluate $g(4)$ , we determine which piece of the piecewise function to use. Since $4$ is in the interval $(-1, 5]$ , we use the second expression.
$g(4) = 2 - (4)$

STEP 11

Calculate the value of $g(4)$ .
$g(4) = 2 - 4 = -2$
The evaluated values are: $\begin{array}{l} g(-4)= 0 \\ g(-2)= 2 \\ g(0)= 2 \\ g(3)= -1 \\ g(4)= -2 \end{array}$

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Evaluate the piecewise function $g(x)$ at different values in its domain: $g(-4), g(-2), g(0), g(3), g(4)$ .

STEP 1

Assumptions
1. The function $g(x)$ is defined piecewise with two different expressions: - $x+4$ for $-5 \leq x \leq -1$ - $2-x$ for $-1 < x \leq 5$
2. We need to evaluate $g(x)$ at specific values: $-4, -2, 0, 3, 4$ .

STEP 2

To evaluate $g(-4)$ , we need to determine which piece of the piecewise function to use. Since $-4$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-4) = (-4) + 4$

STEP 3

Calculate the value of $g(-4)$ .
$g(-4) = -4 + 4 = 0$

STEP 4

To evaluate $g(-2)$ , we again determine which piece of the piecewise function to use. Since $-2$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-2) = (-2) + 4$

STEP 5

Calculate the value of $g(-2)$ .
$g(-2) = -2 + 4 = 2$

STEP 6

To evaluate $g(0)$ , we need to determine which piece of the piecewise function to use. Since $0$ is in the interval $(-1, 5]$ , we use the second expression.
$g(0) = 2 - (0)$

STEP 7

Calculate the value of $g(0)$ .
$g(0) = 2 - 0 = 2$

STEP 8

To evaluate $g(3)$ , we determine which piece of the piecewise function to use. Since $3$ is in the interval $(-1, 5]$ , we use the second expression.
$g(3) = 2 - (3)$

STEP 9

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

STEP 10

To evaluate $g(4)$ , we determine which piece of the piecewise function to use. Since $4$ is in the interval $(-1, 5]$ , we use the second expression.
$g(4) = 2 - (4)$

STEP 11

Calculate the value of $g(4)$ .
$g(4) = 2 - 4 = -2$
The evaluated values are: $\begin{array}{l} g(-4)= 0 \\ g(-2)= 2 \\ g(0)= 2 \\ g(3)= -1 \\ g(4)= -2 \end{array}$

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Evaluate the piecewise function g(x)g(x)g(x) at different values in its domain: g(−4),g(−2),g(0),g(3),g(4)g(-4), g(-2), g(0), g(3), g(4)g(−4),g(−2),g(0),g(3),g(4).

STEP 1

STEP 2

To evaluate g(−4)g(-4)g(−4), we need to determine which piece of the piecewise function to use. Since −4-4−4 is in the interval [−5,−1][-5, -1][−5,−1], we use the first expression.g(−4)=(−4)+4g(-4) = (-4) + 4g(−4)=(−4)+4

STEP 3

Calculate the value of g(−4)g(-4)g(−4).g(−4)=−4+4=0g(-4) = -4 + 4 = 0g(−4)=−4+4=0

STEP 4

To evaluate g(−2)g(-2)g(−2), we again determine which piece of the piecewise function to use. Since −2-2−2 is in the interval [−5,−1][-5, -1][−5,−1], we use the first expression.g(−2)=(−2)+4g(-2) = (-2) + 4g(−2)=(−2)+4

STEP 5

Calculate the value of g(−2)g(-2)g(−2).g(−2)=−2+4=2g(-2) = -2 + 4 = 2g(−2)=−2+4=2

STEP 6

To evaluate g(0)g(0)g(0), we need to determine which piece of the piecewise function to use. Since 000 is in the interval (−1,5](-1, 5](−1,5], we use the second expression.g(0)=2−(0)g(0) = 2 - (0)g(0)=2−(0)

STEP 7

Calculate the value of g(0)g(0)g(0).g(0)=2−0=2g(0) = 2 - 0 = 2g(0)=2−0=2

STEP 8

To evaluate g(3)g(3)g(3), we determine which piece of the piecewise function to use. Since 333 is in the interval (−1,5](-1, 5](−1,5], we use the second expression.g(3)=2−(3)g(3) = 2 - (3)g(3)=2−(3)

STEP 9

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

STEP 10

To evaluate g(4)g(4)g(4), we determine which piece of the piecewise function to use. Since 444 is in the interval (−1,5](-1, 5](−1,5], we use the second expression.g(4)=2−(4)g(4) = 2 - (4)g(4)=2−(4)

STEP 11

Calculate the value of g(4)g(4)g(4).g(4)=2−4=−2g(4) = 2 - 4 = -2g(4)=2−4=−2The evaluated values are: g(−4)=0g(−2)=2g(0)=2g(3)=−1g(4)=−2 \begin{array}{l} g(-4)= 0 \\ g(-2)= 2 \\ g(0)= 2 \\ g(3)= -1 \\ g(4)= -2 \end{array} g(−4)=0g(−2)=2g(0)=2g(3)=−1g(4)=−2​

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Evaluate the piecewise function $g(x)$ at different values in its domain: $g(-4), g(-2), g(0), g(3), g(4)$ .

To evaluate $g(-4)$ , we need to determine which piece of the piecewise function to use. Since $-4$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-4) = (-4) + 4$

Calculate the value of $g(-4)$ .
$g(-4) = -4 + 4 = 0$

To evaluate $g(-2)$ , we again determine which piece of the piecewise function to use. Since $-2$ is in the interval $[-5, -1]$ , we use the first expression.
$g(-2) = (-2) + 4$

Calculate the value of $g(-2)$ .
$g(-2) = -2 + 4 = 2$

To evaluate $g(0)$ , we need to determine which piece of the piecewise function to use. Since $0$ is in the interval $(-1, 5]$ , we use the second expression.
$g(0) = 2 - (0)$

Calculate the value of $g(0)$ .
$g(0) = 2 - 0 = 2$

To evaluate $g(3)$ , we determine which piece of the piecewise function to use. Since $3$ is in the interval $(-1, 5]$ , we use the second expression.
$g(3) = 2 - (3)$

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

To evaluate $g(4)$ , we determine which piece of the piecewise function to use. Since $4$ is in the interval $(-1, 5]$ , we use the second expression.
$g(4) = 2 - (4)$

Calculate the value of $g(4)$ .
$g(4) = 2 - 4 = -2$
The evaluated values are: $\begin{array}{l} g(-4)= 0 \\ g(-2)= 2 \\ g(0)= 2 \\ g(3)= -1 \\ g(4)= -2 \end{array}$