1st Semester Algebra II Concepts Review

Front

What is the DOMAIN of a linear function?

Back

Front

What are decreasing intervals of a function?

Back

Decreasing intervals of a function are the ranges of x-values where the function's output (y-value) decreases as x increases. For example, if a function is decreasing on the interval @@(- inf, 3) U (3, inf)@@, it means the function decreases for all x less than 3 and for all x greater than 3.

Front

How do you determine where a graph is increasing or decreasing?

Back

Front

How do you factor the polynomial 4x^3 + 2x^2 - 6x?

Back

To factor the polynomial 4x^3 + 2x^2 - 6x, first factor out the greatest common factor, which is 2x. This gives you 2x(2x^2 + x - 3). Then, factor the quadratic to get 2x(2x + 3)(x - 1).

Front

What transformations are represented by g(x) = f(-x) - 4?

Back

The transformation g(x) = f(-x) - 4 represents a reflection over the y-axis (due to the -x) and a vertical shift downwards by 4 units.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness and direction, calculated as the change in y divided by the change in x (rise over run). It is often represented by the letter m.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

What does it mean for a function to be increasing?

Back

A function is said to be increasing on an interval if, as the input values (x) increase, the output values (y) also increase. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is said to be decreasing on an interval if, as the input values (x) increase, the output values (y) decrease. This is indicated by a negative slope.