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Answer :

Using translation concepts, we have that the table of values for the function p(x) = x - 7 is given by:

  • x = -2, p(x) = -9.
  • x = -1, p(x) = -8.
  • x = 0, p(x) = -7.
  • x = 1, p(x) = -6.
  • x = 2, p(x) = -5.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

y = f(x).

A translation down 7 units is represented by a subtraction by 7 in the range, that is:

p(x) = f(x) - 7 = x - 7.

The numeric values to be inserted in the table are given by:

  • x = -2, p(x) = -9.
  • x = -1, p(x) = -8.
  • x = 0, p(x) = -7.
  • x = 1, p(x) = -6.
  • x = 2, p(x) = -5.

In the graph at the end of the exercise, both functions are shown.

More can be learned about translation concepts at https://brainly.com/question/28416763

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