Solving Systems of Equations and Absolute Values

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is denoted as f(x) = |x|.

Front

What is the vertex of the absolute value function f(x) = |x - h| + k?

Back

The vertex of the function is the point (h, k), which represents the minimum or maximum point of the graph.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shape, opening upwards if the coefficient of the absolute value is positive and downwards if it is negative.

Front

What is the axis of symmetry for the function f(x) = |x - 3| + 4?

Back

The axis of symmetry is the vertical line x = 3.

Front

How does the transformation y = -|x| affect the graph of y = |x|?

Back

The transformation reflects the graph over the x-axis.

Front

What does the equation |x - a| = b represent?

Back

This equation represents two linear equations: x - a = b and x - a = -b, leading to two solutions.

Front

What is the effect of a vertical stretch on the graph of an absolute value function?

Back

A vertical stretch by a factor of k (where k > 1) makes the V-shape narrower.

Front

How do you write an absolute value equation for a range of values?

Back

To write an absolute value equation for a range, use the form |x - a| = b, where a is the midpoint and b is the distance from a.

Front

What is the parent function of absolute value?

Back

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

Front

What does the transformation y = |x| + k do to the graph?

Back

The transformation shifts the graph of y = |x| vertically by k units.