Transformations of Parent Functions

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 a transformation in the context of functions?

Back

A transformation is an operation that moves or changes a function's graph in some way, such as shifting, reflecting, stretching, or compressing.

Front

How does a horizontal shift affect the graph of a function?

Back

A horizontal shift moves the graph left or right. For example, f(x - h) shifts the graph to the right by h units, while f(x + h) shifts it to the left by h units.

Front

What is the effect of a vertical shift on a function's graph?

Back

A vertical shift moves the graph up or down. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What does it mean to reflect a graph over the y-axis?

Back

Reflecting a graph over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

How do you identify a quadratic function?

Back

A quadratic function is identified by its standard form: f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What is the effect of the coefficient 'a' in the vertex form of a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

How do you determine the transformations of a function from its equation?

Back

To determine transformations, compare the function's equation to its parent function's equation, noting shifts, reflections, and stretches/compressions.