Math / Algebra

Question $\begin{array}{l}h(x)=\left\{\begin{array}{ll}-5 x-17, & \text { for } x<-3 \\ 1, & \text { for }-3 \leq x<1 \\ x+4, & \text { for } x \geq 1\end{array}\right. \\ h(-10)=\square \\ h(-2)=\square \\ h(1)=\square \\ h(4)=\square\end{array}$

Studdy Solution

STEP 1

1. The function $h(x)$ is a piecewise function with different expressions for different intervals of $x$ .
2. We need to evaluate $h(x)$ at specific points: $x = -10$ , $x = -2$ , $x = 1$ , and $x = 4$ .

STEP 2

1. Identify the correct piece of the piecewise function for each given $x$ .
2. Evaluate the function at $x = -10$ .
3. Evaluate the function at $x = -2$ .
4. Evaluate the function at $x = 1$ .
5. Evaluate the function at $x = 4$ .

STEP 3

Identify the correct piece of the piecewise function for each given $x$ :
- For $x < -3$ , use $h(x) = -5x - 17$ . - For $-3 \leq x < 1$ , use $h(x) = 1$ . - For $x \geq 1$ , use $h(x) = x + 4$ .

STEP 4

Evaluate the function at $x = -10$ :
Since $-10 < -3$ , we use $h(x) = -5x - 17$ .
$h(-10) = -5(-10) - 17$ $h(-10) = 50 - 17$ $h(-10) = 33$

STEP 5

Evaluate the function at $x = -2$ :
Since $-3 \leq -2 < 1$ , we use $h(x) = 1$ .
$h(-2) = 1$

STEP 6

Evaluate the function at $x = 1$ :
Since $x = 1$ and $x \geq 1$ , we use $h(x) = x + 4$ .
$h(1) = 1 + 4$ $h(1) = 5$

STEP 7

Evaluate the function at $x = 4$ :
Since $x = 4$ and $x \geq 1$ , we use $h(x) = x + 4$ .
$h(4) = 4 + 4$ $h(4) = 8$
The evaluated values are: $h(-10) = 33$ $h(-2) = 1$ $h(1) = 5$ $h(4) = 8$

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Question $\begin{array}{l}h(x)=\left\{\begin{array}{ll}-5 x-17, & \text { for } x<-3 \\ 1, & \text { for }-3 \leq x<1 \\ x+4, & \text { for } x \geq 1\end{array}\right. \\ h(-10)=\square \\ h(-2)=\square \\ h(1)=\square \\ h(4)=\square\end{array}$

Studdy Solution

STEP 1

1. The function $h(x)$ is a piecewise function with different expressions for different intervals of $x$ .
2. We need to evaluate $h(x)$ at specific points: $x = -10$ , $x = -2$ , $x = 1$ , and $x = 4$ .

STEP 2

1. Identify the correct piece of the piecewise function for each given $x$ .
2. Evaluate the function at $x = -10$ .
3. Evaluate the function at $x = -2$ .
4. Evaluate the function at $x = 1$ .
5. Evaluate the function at $x = 4$ .

STEP 3

Identify the correct piece of the piecewise function for each given $x$ :
- For $x < -3$ , use $h(x) = -5x - 17$ . - For $-3 \leq x < 1$ , use $h(x) = 1$ . - For $x \geq 1$ , use $h(x) = x + 4$ .

STEP 4

Evaluate the function at $x = -10$ :
Since $-10 < -3$ , we use $h(x) = -5x - 17$ .
$h(-10) = -5(-10) - 17$ $h(-10) = 50 - 17$ $h(-10) = 33$

STEP 5

Evaluate the function at $x = -2$ :
Since $-3 \leq -2 < 1$ , we use $h(x) = 1$ .
$h(-2) = 1$

STEP 6

Evaluate the function at $x = 1$ :
Since $x = 1$ and $x \geq 1$ , we use $h(x) = x + 4$ .
$h(1) = 1 + 4$ $h(1) = 5$

STEP 7

Evaluate the function at $x = 4$ :
Since $x = 4$ and $x \geq 1$ , we use $h(x) = x + 4$ .
$h(4) = 4 + 4$ $h(4) = 8$
The evaluated values are: $h(-10) = 33$ $h(-2) = 1$ $h(1) = 5$ $h(4) = 8$

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Studdy Solution

STEP 1

1. The function h(x) h(x) h(x) is a piecewise function with different expressions for different intervals of x x x.2. We need to evaluate h(x) h(x) h(x) at specific points: x=−10 x = -10 x=−10, x=−2 x = -2 x=−2, x=1 x = 1 x=1, and x=4 x = 4 x=4.

STEP 2

1. Identify the correct piece of the piecewise function for each given x x x.2. Evaluate the function at x=−10 x = -10 x=−10.3. Evaluate the function at x=−2 x = -2 x=−2.4. Evaluate the function at x=1 x = 1 x=1.5. Evaluate the function at x=4 x = 4 x=4.

STEP 3

Identify the correct piece of the piecewise function for each given x x x:- For x<−3 x < -3 x<−3, use h(x)=−5x−17 h(x) = -5x - 17 h(x)=−5x−17. - For −3≤x<1 -3 \leq x < 1 −3≤x<1, use h(x)=1 h(x) = 1 h(x)=1. - For x≥1 x \geq 1 x≥1, use h(x)=x+4 h(x) = x + 4 h(x)=x+4.

STEP 4

STEP 5

Evaluate the function at x=−2 x = -2 x=−2:Since −3≤−2<1 -3 \leq -2 < 1 −3≤−2<1, we use h(x)=1 h(x) = 1 h(x)=1.h(−2)=1 h(-2) = 1 h(−2)=1

STEP 6

Evaluate the function at x=1 x = 1 x=1:Since x=1 x = 1 x=1 and x≥1 x \geq 1 x≥1, we use h(x)=x+4 h(x) = x + 4 h(x)=x+4.h(1)=1+4 h(1) = 1 + 4 h(1)=1+4 h(1)=5 h(1) = 5 h(1)=5

STEP 7

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1. The function $h(x)$ is a piecewise function with different expressions for different intervals of $x$ .
2. We need to evaluate $h(x)$ at specific points: $x = -10$ , $x = -2$ , $x = 1$ , and $x = 4$ .

1. Identify the correct piece of the piecewise function for each given $x$ .
2. Evaluate the function at $x = -10$ .
3. Evaluate the function at $x = -2$ .
4. Evaluate the function at $x = 1$ .
5. Evaluate the function at $x = 4$ .

Identify the correct piece of the piecewise function for each given $x$ :
- For $x < -3$ , use $h(x) = -5x - 17$ . - For $-3 \leq x < 1$ , use $h(x) = 1$ . - For $x \geq 1$ , use $h(x) = x + 4$ .

Evaluate the function at $x = -2$ :
Since $-3 \leq -2 < 1$ , we use $h(x) = 1$ .
$h(-2) = 1$

Evaluate the function at $x = 1$ :
Since $x = 1$ and $x \geq 1$ , we use $h(x) = x + 4$ .
$h(1) = 1 + 4$ $h(1) = 5$