Graph this function. f(x) = -3x - 11 if -6 ≤ x ≤

Questions: Graph this function. f(x) = -3x - 11 if -6 ≤ x ≤ -4 -1/4 x if -4 < x ≤ 8

Transcript text: Graph this function. \[ f(x)=\left\{\begin{array}{ll} -3 x-11 & \text { if }-6 \leq x \leq-4 \\ -\frac{1}{4} x & \text { if }-4

Solution

Solution Steps

Step 1: Evaluate the first piece of the function at the endpoints of its interval

The first piece of the function is \(f(x) = -3x - 11\) for \(-6 \le x \le -4\). When \(x = -6\), \(f(-6) = -3(-6) - 11 = 18 - 11 = 7\). So, we have the point \((-6, 7)\). When \(x = -4\), \(f(-4) = -3(-4) - 11 = 12 - 11 = 1\). So, we have the point \((-4, 1)\).

Step 2: Evaluate the second piece of the function at the endpoints of its interval

The second piece of the function is \(f(x) = -\frac{1}{4}x\) for \(-4 < x \le 8\). When \(x = -4\), \(f(-4) = -\frac{1}{4}(-4) = 1\). So, we have the point \((-4, 1)\). This point is an open circle since \(x\) cannot be equal to \(-4\) for this piece. When \(x = 8\), \(f(8) = -\frac{1}{4}(8) = -2\). So, we have the point \((8, -2)\).

Step 3: Plot the points and connect them

Plot the points \((-6, 7)\) and \((-4, 1)\) and connect them with a line segment. Since the interval is \(-6 \le x \le -4\), the points are closed circles.

Plot the points \((-4, 1)\) as an open circle and \((8, -2)\) as a closed circle and connect them with a line segment.

Final Answer

The graph consists of two line segments. The first segment connects \((-6, 7)\) and \((-4, 1)\) with closed circles at both endpoints. The second segment connects \((-4, 1)\) with an open circle and \((8, -2)\) with a closed circle. \\( \boxed{ \text{See the graph below}} \\)

      y
      ^
      |
    8 -
      |
    7 -   *
      |       *
    6 -           *
      |               *
    5 -                   *
      |                       *
    4 -                           *
      |                               *
    3 -                                   *
      |
    2 -                                       *
      |
    1 - ---------------------o-----------------------*
      |
    0 -                         |
      |
  -1 -                         |
      |
  -2 -                         |
      |
  -3 -                         |
      |
  -4 -                         |
      |
  -5 -                         |
      |
  -6 -*------------------------|-----------------------+----> x
      |                         -4                        8
  -7 -
      |
  -8 -
      |

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Questions: Graph this function. f(x) = -3x - 11 if -6 ≤ x ≤ -4 -1/4 x if -4 < x ≤ 8

Solution

Solution Steps

Final Answer

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