H. Algebra 2 Unit Assessment 1 Review

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What is a constant function?

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A constant function is a function that does not change its value regardless of the input. It can be represented as f(x) = c, where c is a constant.

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How do you find the product of two functions f(x) and g(x)?

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To find the product of two functions, multiply their outputs: (f ⋅ g)(x) = f(x) * g(x). For example, if f(x) = 4x + 8 and g(x) = x + 3, then (f ⋅ g)(x) = (4x + 8)(x + 3).

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What are inverse functions?

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Inverse functions are two functions that 'undo' each other. If f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

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How do you determine if two functions are inverses?

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To verify if f(x) and g(x) are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

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What is the difference between two functions g(a) and h(a)?

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The difference of two functions is found by subtracting their outputs: (g - h)(a) = g(a) - h(a). For example, if g(a) = 4a^2 + 11a + 8 and h(a) = 5a^2 + 9a + 3, then (g - h)(a) = -a^2 + 2a + 5.

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What is an interval in mathematics?

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An interval is a range of numbers between two endpoints. For example, (2, 5) is an interval that includes all numbers greater than 2 and less than 5.

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What does it mean for a function to be constant on an interval?

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A function is constant on an interval if it takes the same value for every input within that interval.

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How do you graph the inverse of a function?

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To graph the inverse of a function, reflect the original graph over the line y = x.

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What is the standard form of a quadratic function?

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The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

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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.