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Let the function have domain \-2,-1,0,1,2\ and be defined by f(x)=x². (a) Show the table of the function and (b) What is the range of the function?

Mathematics

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Answer

b

{0,1,4,9}\{0, 1, 4, 9\}

Graph of f(x) = x²

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Key points of f(x) = x²
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Step-by-step solution

5 steps

Here is the solution to the problem.

Part a· 3 steps

Show the table of the function

  1. Identify the domain and the function definition.

    The domain is D={−2,−1,0,1,2,3}D = \{-2, -1, 0, 1, 2, 3\}.
    The function is defined by f(x)=x2f(x) = x^2.

  2. Calculate f(x)f(x) for each value in the domain.

    For x=−2x = -2, f(−2)=(−2)2=4f(-2) = (-2)^2 = 4
    For x=−1x = -1, f(−1)=(−1)2=1f(-1) = (-1)^2 = 1
    For x=0x = 0, f(0)=(0)2=0f(0) = (0)^2 = 0
    For x=1x = 1, f(1)=(1)2=1f(1) = (1)^2 = 1
    For x=2x = 2, f(2)=(2)2=4f(2) = (2)^2 = 4
    For x=3x = 3, f(3)=(3)2=9f(3) = (3)^2 = 9

  3. Create the table.

    xf(x)=x2−24−1100112439\begin{array}{|c|c|} \hline x & f(x) = x^2 \\ \hline -2 & 4 \\ -1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ 3 & 9 \\ \hline \end{array}

Part b

{0,1,4,9}\{0, 1, 4, 9\}

What is the range of the function

  1. List all the output values from the table in part (a).

    The output values are {4,1,0,1,4,9}\{4, 1, 0, 1, 4, 9\}.

  2. Identify the unique values and list them in ascending order.

    The unique values are 0,1,4,90, 1, 4, 9.

    The range of the function is {0,1,4,9}\boxed{\{0, 1, 4, 9\}}.

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