*Algebra Final Review Day 8 (Sect 3, Top 8,9)

Front

What is the Law of Exponents?

Back

The Law of Exponents refers to the rules that govern how to handle mathematical operations involving powers or exponents. For example, a^m * a^n = a^(m+n) and (a^m)^n = a^(m*n).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, if a function is defined for all real numbers, its domain is all real numbers.

Front

How do you find the average rate of change of a function?

Back

The average rate of change of a function f(x) over an interval [a, b] is calculated using the formula: (f(b) - f(a)) / (b - a).

Front

Given f(x) = 2x^2 + 12x + 16, what is the average rate of change on the interval [-3, -2]?

Back

The average rate of change is 2.

Front

What is an absolute minimum point of a function?

Back

An absolute minimum point of a function is the point at which the function takes its lowest value over its entire domain.

Front

What does it mean for a function to have no absolute minimum?

Back

A function has no absolute minimum if it does not reach a lowest value within its domain, often occurring in functions that decrease indefinitely.

Front

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

Back

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

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing on an interval if the output values (y-values) rise as the input values (x-values) increase. It is decreasing if the output values fall as the input values increase.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the range of a function?

Back

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