Vertex and Transformations of Absolute Value Functions

Front

What is the vertex of an absolute value function?

Back

The vertex is the highest or lowest point of the graph of the function, representing the minimum or maximum value.

Front

What is the parent function of absolute value?

Back

The parent function is f(x) = |x|, which creates a V-shaped graph.

Front

How does the graph of f(x) = |x| + k transform the parent function?

Back

The graph shifts vertically up by k units if k is positive and down by k units if k is negative.

Front

What effect does a negative sign in front of the absolute value have on the graph?

Back

It reflects the graph across the x-axis.

Front

What does the equation f(x) = |x - h| + k represent?

Back

This represents a transformation of the parent function, shifting it horizontally by h units and vertically by k units.

Front

How do you find the vertex of the function y = a|x - h| + k?

Back

The vertex is at the point (h, k).

Front

What transformation does f(x) = |x| - 5 represent?

Back

It shifts the graph of the parent function down by 5 units.

Front

What is the effect of the coefficient 'a' in the function f(x) = a|x|?

Back

If |a| > 1, the graph is vertically stretched; if 0 < |a| < 1, it is vertically compressed.

Front

What does the transformation 'right 3, up 2' mean for the function f(x) = |x|?

Back

The function becomes f(x) = |x - 3| + 2.

Front

How do you determine if a function shifts left or right?

Back

If the equation is f(x) = |x + h|, it shifts left by h units; if f(x) = |x - h|, it shifts right by h units.