2023 Fall Semester Exam Review #2

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction; it cannot be written as a ratio of two integers.

Front

Evaluate the function g when x = 4 if g(x) = 5x - 1.

Back

g(4) = 5(4) - 1 = 20 - 1 = 19.

Front

What does it mean for a system of linear equations to have one solution?

Back

It means that the two lines represented by the equations intersect at exactly one point.

Front

What is the solution set of a system of equations?

Back

The solution set is the set of all possible solutions that satisfy all equations in the system.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the coordinates of the point into each equation. If all equations are satisfied, the point is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means that the lines have the same slope but different y-intercepts, resulting in no solutions.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.