Precalc H Semester 1 Final Exam Review Units 1-3 (22-23)

Front

What are the types of discontinuities in a function?

Back

1. Jump Discontinuity: Occurs when the left-hand limit and right-hand limit exist but are not equal. 2. Infinite Discontinuity: Occurs when the function approaches infinity at a certain point. 3. Removable Discontinuity: Occurs when a limit exists at a point, but the function is not defined there.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the polynomial equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or synthetic division.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial of lower degree that divides the polynomial without leaving a remainder. For example, if (x + 4) is a factor of f(x), then f(-4) = 0.

Tags

CCSS.HSA.APR.B.2

Front

What is the significance of the multiplicity of a root?

Back

The multiplicity of a root indicates how many times that root is repeated in the polynomial. A root with an even multiplicity will touch the x-axis and turn around, while a root with an odd multiplicity will cross the x-axis.

Front

How do you determine where a function is less than zero?

Back

To determine where a function is less than zero, find the intervals where the function's graph lies below the x-axis. This can be done by finding the zeros of the function and testing intervals between them.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity can be 'fixed' by redefining the function at that point, while a non-removable discontinuity cannot be fixed and indicates a more severe break in the function.

Tags

CCSS.HSF-IF.C.7D

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation with integer coefficients is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2

Front

How do you use synthetic division to find polynomial zeros?

Back

To use synthetic division, set the polynomial equal to zero to find a potential root. Then, perform synthetic division with that root. If the remainder is zero, the root is confirmed.

Front

What is the Fundamental Theorem of Algebra?

Back

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.

Tags

CCSS.HSN.CN.C.9