Flashcard - Friday, November 15th

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|.

Front

How do you solve an equation involving absolute value, such as |x - a| = b?

Back

To solve |x - a| = b, you set up two equations: x - a = b and x - a = -b, then solve for x.

Front

What does the expression |x - 12| - 3 = 11 represent?

Back

It represents an absolute value equation that can be solved by isolating the absolute value expression.

Front

What are the steps to solve the equation |x - 12| - 3 = 11?

Back

1. Add 3 to both sides: |x - 12| = 14. 2. Set up two equations: x - 12 = 14 and x - 12 = -14. 3. Solve for x: x = 26 and x = -2.

Front

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

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

What is the graphical representation of the absolute value function y = |x|?

Back

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

Front

How does the graph of y = |x| - 8 differ from y = |x|?

Back

The graph of y = |x| - 8 is shifted down 8 units from the graph of y = |x|.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph.

Front

What is the significance of the vertex in an absolute value function?

Back

The vertex is the point where the graph changes direction and is the minimum or maximum point of the function.

Front

How do you determine the number of solutions for a system of linear equations?

Back

You can determine the number of solutions by analyzing the slopes and intercepts of the lines: one solution (intersecting), no solution (parallel), or infinitely many solutions (same line).