QuestionGraph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

Studdy Solution

STEP 1

Assumptions1. The function is defined piecewise, with three different expressions for different ranges of x. . The function is continuous within its defined intervals.
3. The function is defined for all real numbers.

STEP 2

We will graph each piece of the function separately. Let's start with the first piece, $f(x) =4$ for $x \leq -1$ . This is a horizontal line at $y =4$ for $x \leq -1$ .

STEP 3

To graph this piece, we plot a point at $(-1,)$ and draw a horizontal line to the left of this point. The point at $(-1,)$ should be a filled circle because the function is defined at $x = -1$ .

STEP 4

Next, we graph the second piece of the function, $f(x) = x +3$ for $-1 < x <4$ . This is a linear function with slope1 and y-intercept3.

STEP 5

To graph this piece, we plot points at $(-1,2)$ and $(4,7)$ and draw a line through these points. The points at $(-1,2)$ and $(4,7)$ should be open circles because the function is not defined at $x = -1$ and $x =4$ .

STEP 6

Finally, we graph the third piece of the function, $f(x) =2x -2$ for $x \geq4$ . This is a linear function with slope2 and y-intercept -2.

STEP 7

To graph this piece, we plot a point at $(4,6)$ and draw a line with slope2 to the right of this point. The point at $(4,6)$ should be a filled circle because the function is defined at $x =4$ .

STEP 8

By combining the three pieces, we obtain the graph of the function $f(x)$ .

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QuestionGraph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

Studdy Solution

STEP 1

Assumptions1. The function is defined piecewise, with three different expressions for different ranges of x. . The function is continuous within its defined intervals.
3. The function is defined for all real numbers.

STEP 2

We will graph each piece of the function separately. Let's start with the first piece, $f(x) =4$ for $x \leq -1$ . This is a horizontal line at $y =4$ for $x \leq -1$ .

STEP 3

To graph this piece, we plot a point at $(-1,)$ and draw a horizontal line to the left of this point. The point at $(-1,)$ should be a filled circle because the function is defined at $x = -1$ .

STEP 4

Next, we graph the second piece of the function, $f(x) = x +3$ for $-1 < x <4$ . This is a linear function with slope1 and y-intercept3.

STEP 5

To graph this piece, we plot points at $(-1,2)$ and $(4,7)$ and draw a line through these points. The points at $(-1,2)$ and $(4,7)$ should be open circles because the function is not defined at $x = -1$ and $x =4$ .

STEP 6

Finally, we graph the third piece of the function, $f(x) =2x -2$ for $x \geq4$ . This is a linear function with slope2 and y-intercept -2.

STEP 7

To graph this piece, we plot a point at $(4,6)$ and draw a line with slope2 to the right of this point. The point at $(4,6)$ should be a filled circle because the function is defined at $x =4$ .

STEP 8

By combining the three pieces, we obtain the graph of the function $f(x)$ .

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QuestionGraph the piecewise function: f(x)={4for x≤−1x+3for −1<x<42x−2for x≥4 f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases} f(x)=⎩⎨⎧​4x+32x−2​for x≤−1for −1<x<4for x≥4​

Studdy Solution

STEP 1

Assumptions1. The function is defined piecewise, with three different expressions for different ranges of x. . The function is continuous within its defined intervals.3. The function is defined for all real numbers.

STEP 2

We will graph each piece of the function separately. Let's start with the first piece, f(x)=4f(x) =4f(x)=4 for x≤−1x \leq -1x≤−1. This is a horizontal line at y=4y =4y=4 for x≤−1x \leq -1x≤−1.

STEP 3

To graph this piece, we plot a point at (−1,)(-1,)(−1,) and draw a horizontal line to the left of this point. The point at (−1,)(-1,)(−1,) should be a filled circle because the function is defined at x=−1x = -1x=−1.

STEP 4

Next, we graph the second piece of the function, f(x)=x+3f(x) = x +3f(x)=x+3 for −1<x<4-1 < x <4−1<x<4. This is a linear function with slope1 and y-intercept3.

STEP 5

To graph this piece, we plot points at (−1,2)(-1,2)(−1,2) and (4,7)(4,7)(4,7) and draw a line through these points. The points at (−1,2)(-1,2)(−1,2) and (4,7)(4,7)(4,7) should be open circles because the function is not defined at x=−1x = -1x=−1 and x=4x =4x=4.

STEP 6

Finally, we graph the third piece of the function, f(x)=2x−2f(x) =2x -2f(x)=2x−2 for x≥4x \geq4x≥4. This is a linear function with slope2 and y-intercept -2.

STEP 7

To graph this piece, we plot a point at (4,6)(4,6)(4,6) and draw a line with slope2 to the right of this point. The point at (4,6)(4,6)(4,6) should be a filled circle because the function is defined at x=4x =4x=4.

STEP 8

By combining the three pieces, we obtain the graph of the function f(x)f(x)f(x).

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QuestionGraph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

Assumptions1. The function is defined piecewise, with three different expressions for different ranges of x. . The function is continuous within its defined intervals.
3. The function is defined for all real numbers.

We will graph each piece of the function separately. Let's start with the first piece, $f(x) =4$ for $x \leq -1$ . This is a horizontal line at $y =4$ for $x \leq -1$ .

To graph this piece, we plot a point at $(-1,)$ and draw a horizontal line to the left of this point. The point at $(-1,)$ should be a filled circle because the function is defined at $x = -1$ .

Next, we graph the second piece of the function, $f(x) = x +3$ for $-1 < x <4$ . This is a linear function with slope1 and y-intercept3.

To graph this piece, we plot points at $(-1,2)$ and $(4,7)$ and draw a line through these points. The points at $(-1,2)$ and $(4,7)$ should be open circles because the function is not defined at $x = -1$ and $x =4$ .

Finally, we graph the third piece of the function, $f(x) =2x -2$ for $x \geq4$ . This is a linear function with slope2 and y-intercept -2.

To graph this piece, we plot a point at $(4,6)$ and draw a line with slope2 to the right of this point. The point at $(4,6)$ should be a filled circle because the function is defined at $x =4$ .

By combining the three pieces, we obtain the graph of the function $f(x)$ .