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Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)x f(x) = 52 −x −2−1 0 1 2

Question

Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)

  • x
  • f(x) = 52 - x
  • -2
  • -1
  • 0
  • 1
  • 2
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Solution

1. Break Down the Problem

We need to evaluate the function f(x)=52x f(x) = 52 - x at the specified values of x x : -2, -1, 0, 1, and 2. We will construct a table of values from these computations.

2. Relevant Concepts

The function given is linear, and we can calculate f(x) f(x) using direct substitution. The rounded values will be calculated to three decimal places.

3. Analysis and Detail

We will compute f(x) f(x) for each of the given x x values:

  1. For x=2 x = -2 : f(2)=52(2)=52+2=54 f(-2) = 52 - (-2) = 52 + 2 = 54

  2. For x=1 x = -1 : f(1)=52(1)=52+1=53 f(-1) = 52 - (-1) = 52 + 1 = 53

  3. For x=0 x = 0 : f(0)=520=52 f(0) = 52 - 0 = 52

  4. For x=1 x = 1 : f(1)=521=51 f(1) = 52 - 1 = 51

  5. For x=2 x = 2 : f(2)=522=50 f(2) = 52 - 2 = 50

4. Verify and Summarize

Now, let's summarize the computed values and present them in a table format.

Final Answer

x x f(x) f(x)
-2 54.000
-1 53.000
0 52.000
1 51.000
2 50.000

Thus, the table of values for the function f(x)=52x f(x) = 52 - x rounded to three decimal places is as shown above.

This problem has been solved

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