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The function H is defined as follows for the domain given.

h (x) = 1 - 2x, domain = {-3, -2, 1, 5}
Write the range of H using set notation. Then graph H.

1 answer

To find the range of the function \( h(x) = 1 - 2x \) for the specified domain \( {-3, -2, 1, 5} \), we will calculate the value of \( h(x) \) for each element in the domain:

  1. For \( x = -3 \): \[ h(-3) = 1 - 2(-3) = 1 + 6 = 7 \]

  2. For \( x = -2 \): \[ h(-2) = 1 - 2(-2) = 1 + 4 = 5 \]

  3. For \( x = 1 \): \[ h(1) = 1 - 2(1) = 1 - 2 = -1 \]

  4. For \( x = 5 \): \[ h(5) = 1 - 2(5) = 1 - 10 = -9 \]

Now we compile the output values:

  • \( h(-3) = 7 \)
  • \( h(-2) = 5 \)
  • \( h(1) = -1 \)
  • \( h(5) = -9 \)

Thus, the range of \( h \) can be written using set notation: \[ \text{Range}(h) = {-9, -1, 5, 7} \]

Graph of \( h \)

Now, we will represent the function in graph form. Given that \( h \) is defined for a discrete set of points, the graph will consist of points corresponding to the domain and their associated outputs.

\[ \text{Points to plot: } (-3, 7), (-2, 5), (1, -1), (5, -9) \]

Here's a rough sketch of the graph:

   |
  8|             *
  7|             |
  6|             |
  5|         *   |
  4|             |
  3|             |
  2|             |
  1|             |
   |_____________________
 -3 -2  0  1  2  3  4  5
   |                 *
 -1|             |
   |             |
 -2|             |
 -3|             |
 -4|             |
 -5|             |
 -6|             |
 -7|             |
 -8|             |
 -9|         *

Each asterisk (*) represents a point on the graph of \( h(x) \) corresponding to its calculated values. The points are:

  • (-3, 7)
  • (-2, 5)
  • (1, -1)
  • (5, -9)

That's the entire analysis including calculation of the range and a graph representation of the function!