Chapter 1 Flashcard 4 ( 1.6 - 1.10)

Front

What are domain restrictions in a function?

Back

Domain restrictions define the set of input values (x-values) for which a function is defined. For example, in the function piece defined as 1 ≤ x < 3, x can only take values between 1 and 3, including 1 but not 3.

Front

Solve for x and y using substitution: x = 1 - 4y and 2x + 7y = 3.

Back

x = 5, y = -1.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

Solve the system of equations by elimination: x + y = 7 and x - y = -1.

Back

x = 3, y = 4.

Front

What does the notation (-∞, -1) U (3, ∞) represent?

Back

This notation represents the union of two intervals: all real numbers less than -1 and all real numbers greater than 3.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope and y-intercept, then use the slope-intercept form: y = mx + b.

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 the symbol U represent in interval notation?

Back

The symbol U represents the union of two sets or intervals, indicating that values from both sets are included.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.