Absolute Value Graphs and Transformations

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|, where |x| is the distance of x from 0 on the number line.

Front

What does the graph of f(x) = |x| look like?

Back

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

Front

What effect does a negative sign in front of an absolute value function have on its graph?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis.

Front

How does the equation f(x) = |x - h| + k transform the graph of f(x) = |x|?

Back

The graph is shifted horizontally by h units and vertically by k units. If h is positive, the graph shifts right; if h is negative, it shifts left. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What is the transformation represented by f(x + 3)?

Back

The transformation f(x + 3) shifts the graph of f(x) 3 units to the left.

Front

What is the transformation represented by f(x) - 4?

Back

The transformation f(x) - 4 shifts the graph of f(x) 4 units down.

Front

Given the function f(x) = |x|, what is the new function after a vertical stretch by a factor of 2?

Back

The new function is f(x) = 2|x|.

Front

What is the effect of adding a constant outside the absolute value, such as in f(x) = |x| + 5?

Back

Adding a constant outside the absolute value shifts the graph vertically upwards by that constant.

Front

What does the transformation f(x - 1) + 2 represent?

Back

The transformation f(x - 1) + 2 shifts the graph 1 unit to the right and 2 units up.

Front

How do you determine the vertex of the absolute value function f(x) = -|x + 2| + 3?

Back

The vertex can be found at the point (-2, 3), which is derived from the transformations applied to the basic absolute value function.