Pre-Calculus Post Test 1 Review 24/25

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What does it mean for a function to be increasing?

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A function is increasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is less than the function value at x2 (f(x1) < f(x2)).

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What does it mean for a function to be decreasing?

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A function is decreasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is greater than the function value at x2 (f(x1) > f(x2)).

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How do you determine the intervals of increase and decrease for a function?

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To determine intervals of increase and decrease, find the derivative of the function. Set the derivative to zero to find critical points, then test intervals around these points to see where the derivative is positive (increasing) or negative (decreasing).

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What is the definition of an even function?

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A function f(x) is even if for every x in the domain, f(-x) = f(x). This means the graph of the function is symmetric about the y-axis.

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What is the definition of an odd function?

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A function f(x) is odd if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric about the origin.

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What is the domain of a function?

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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.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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Front

What is the relationship between logarithms and exponents?

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What is a critical point in calculus?

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A critical point of a function is a point where the derivative is zero or undefined. It is where the function may change from increasing to decreasing or vice versa.