Flashcard - Friday, November 15th

Front

What is the definition of an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

What does the notation y ≤ 5x - 1 represent?

Back

It represents all the points (x, y) that lie on or below the line defined by the equation y = 5x - 1.

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What does a vertical shift of a function mean?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

What is the effect of adding a constant to the absolute value function?

Back

Adding a constant to the absolute value function shifts the graph vertically. For example, f(x) = |x| + 4 shifts the graph up by 4 units.

Front

What does it mean for two lines to be identical?

Back

Identical lines are lines that lie on top of each other, meaning they have the same slope and y-intercept, resulting in infinitely many solutions.

Front

What is the solution to a system of linear equations?

Back

The solution to a system of linear equations is the point (or points) where the graphs of the equations intersect.

Front

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

Back

It means that the lines represented by the equations are parallel and will never intersect.

Front

What is the graphical representation of the equation f(x) = |x|?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards with its vertex at the origin (0,0).