Parent Functions, Attributes, Graphs, and Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What is the parent function of absolute value?

Back

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

Front

What transformation is represented by f(x) = -|x|?

Back

This represents a reflection of the absolute value function across the x-axis.

Front

What does the equation f(x) = |x - 1| + 4 represent?

Back

This represents a vertical shift of the absolute value function up by 4 units and a horizontal shift to the right by 1 unit.

Front

What is the range of the function f(x) = |x|?

Back

The range is [0, ∞) because the absolute value function outputs non-negative values.

Front

How does the coefficient affect the graph of f(x) = a|x|?

Back

The coefficient 'a' affects the vertical stretch or compression and the direction of the graph (if 'a' is negative, it reflects across the x-axis).

Front

What is the vertex of the function f(x) = -3|x - 1| + 4?

Back

The vertex is at the point (1, 4) because it is the point where the graph changes direction.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function results in a vertical shift of the graph.

Front

What is the equation of the graph that opens downwards and has a vertex at (2, 4)?

Back

The equation is y = -|x - 2| + 4.

Front

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

Back

This represents a transformation of the parent absolute value function, where (h, k) is the vertex and 'a' affects the direction and stretch.