ALGEBRA 2

Domain of the Function

  • The domain of the function in question (denoted as (x^3)) is identified to be all real numbers.

    • Reasoning:

    • The function does not contain any square roots, which could restrict the values of (x).

    • There are no divisions by zero, which often limits the domain of a function.

    • No rational exponents or other forms that typically implicate restrictions on the input values are present.

Evaluation of Function at Specific Point

  • The final task outlined in the discussion is to evaluate the function when (x = -2).

    • Procedure:

    • Substitute (-2) into the function, replacing every instance of (x) with (-2).

    • This results in the expression:
      2 \times (-2)^3 + (-2)^2 - 4 \times (-2) + 7

Step-by-Step Simplification

  • Each term in the expression needs simplification as follows:

    • First Term: (-2^3 = -2 \times -2 \times -2 = -8)

    • Calculation Break Down:

      • (-2 \times -2 = 4) (first two factors)

      • Then (4 \times -2 = -8)

    • Second Term: ((-2)^2 = -2 \times -2 = 4)

    • Third Term: (-4 \times -2 = 8) (negative multiplied by negative gives a positive result)

    • Fourth Term: Constant term equals to (7)

  • Combining all the simplified terms:

    • The full expression to evaluate becomes:
      -8 + 4 + 8 + 7

    • This simplifies as follows:

    • Combine the values:

      • Start with (-8 + 4 = -4)

      • Add (8): (-4 + 8 = 4)

      • Finally add (7): (4 + 7 = 11)

Result of Evaluation

  • Therefore, the evaluated result when (x = -2) is:
    g(-2) = 11

Recommendations During Assessment

  • It is advised, during tests such as the ACT or any math evaluation:

    • Reduce potential errors by utilizing a calculator for complex computations once simplified.

    • Maintain clarity by either simplifying the expression entirely or stopping after reaching a point where using a calculator is feasible.

    • Typing everything correctly into a calculator helps in avoiding mistakes:

    • Ensure all parentheses are appropriately added to avoid any computation errors.

  • Note:

    • Mistakes are a normal part of the math process; thus, exercising care while entering values into the calculator is crucial for accurate results.

Importance of Practice

  • Continuous practice is emphasized as essential for mastery in evaluating problems of this nature.

    • Resources such as Canvas can be utilized to access additional practice materials and questions related to this topic for further skill enhancement.