Absolute Value Graphs

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you evaluate the absolute value of a number?

Back

To evaluate the absolute value of a number, remove any negative sign. For example, |−5| = 5 and |5| = 5.

Front

What is the general shape of the graph of an absolute value function?

Back

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

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 point of the graph.

Front

How does the parameter 'h' affect the graph of f(x) = |x - h|?

Back

The parameter 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

How does the parameter 'k' affect the graph of f(x) = |x - h| + k?

Back

The parameter 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the equation of the absolute value function that has a vertex at (3, 1)?

Back

The equation is f(x) = |x - 3| + 1.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If any x-value is paired with more than one y-value, it is not a function.

Front

Evaluate f(33) for the function f(x) = |x - 22|.

Back

f(33) = |33 - 22| = |11| = 11.

Front

What is the effect of multiplying an absolute value function by a negative number?

Back

Multiplying an absolute value function by a negative number reflects the graph across the x-axis.