Coll. Alg. Ch. 1,2 1st Sem. Rev. 2020

Front

What is the definition of x-axis symmetry?

Back

A function has x-axis symmetry if for every point (x, y) on the graph, the point (x, -y) is also on the graph.

Front

What are critical values in a function?

Back

Critical values are the values of x where the derivative of the function is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

How do you determine if a function is decreasing over an interval?

Back

A function is decreasing over an interval if the derivative is negative for all x in that interval.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f, denoted as f^(-1)(x), such that f(f^(-1)(x)) = x.

Front

How can you show that a function has y-axis symmetry?

Back

A function has y-axis symmetry if substituting -x for x in the function yields the same function, i.e., f(-x) = f(x).

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as 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 does it mean for a function to be increasing?

Back

A function is increasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

How do you find the critical points of a function?

Back

To find critical points, take the derivative of the function, set it equal to zero, and solve for x.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial determines its end behavior: even degree polynomials have the same end behavior, while odd degree polynomials have opposite end behavior.