AP Precalculus Unit 1 & 2 Review

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What is the average rate of change of a function on an interval?

Back

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

A function f(x) is said to be increasing on an interval (a, b) if for any two points x1 and x2 in (a, b), where x1 < x2, it holds that f(x1) < f(x2).

Front

What is the definition of a positive function?

Back

A function f(x) is positive on an interval (a, b) if for all x in (a, b), f(x) > 0.

Tags

CCSS.HSF.LE.B.5

Front

How do you determine the intervals where a function is increasing or decreasing?

Back

To determine the intervals where a function is increasing or decreasing, find the derivative f'(x). The function is increasing where f'(x) > 0 and decreasing where f'(x) < 0.

Front

What is a root of a polynomial function?

Back

A root of a polynomial function is a value of x for which the polynomial evaluates to zero, i.e., f(x) = 0.

Tags

CCSS.HSF-IF.C.7C

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear and/or irreducible quadratic factors, based on its roots.

Tags

CCSS.HSA.APR.B.2

Front

What is an extremum in calculus?

Back

An extremum is a point in the domain of a function where the function takes on a maximum or minimum value.

Front

How do you find the number of extrema of a function?

Back

To find the number of extrema, analyze the critical points by setting the derivative f'(x) to zero and determining the sign changes.

Front

What is the significance of complex roots in polynomial functions?

Back

Complex roots occur in conjugate pairs and indicate that the polynomial does not cross the x-axis at those points, affecting the graph's behavior.

Tags

CCSS.HSN.CN.C.9

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

A polynomial of degree n has exactly n roots, counting multiplicities, which may be real or complex.