Precalculus First Semester Exam Review

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What is the composition of functions?

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The composition of functions is a way to combine two functions where the output of one function becomes the input of another. If f(x) and g(x) are two functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).

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How do you evaluate a function at a specific point?

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To evaluate a function at a specific point, substitute the value of the variable into the function's equation. For example, if f(x) = 2x and you want to find f(3), calculate f(3) = 2(3) = 6.

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What is the Fundamental Theorem of Algebra?

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The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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How do you convert a quadratic function to vertex form?

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To convert a quadratic function from standard form (y = ax^2 + bx + c) to vertex form (y = a(x-h)^2 + k), complete the square.

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial, similar to numerical long division, resulting in a quotient and a remainder.

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What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. For the quadratic function y = ax^2 + bx + c, the vertex can be found at the point (h, k) where h = -b/(2a) and k = f(h).

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What is the difference between a rational and an irrational number?

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A rational number can be expressed as a fraction of two integers (e.g., 1/2, 3, -4), while an irrational number cannot be expressed as a simple fraction (e.g., √2, π).

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What is the quadratic formula?

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The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

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What is a function's domain?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.