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 can be transformed to create other functions in that family.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally, vertically, or both without changing its shape.

Front

How do you translate a function up by 'k' units?

Back

To translate a function up by 'k' units, you add 'k' to the function: f(x) becomes f(x) + k.

Front

How do you translate a function down by 'k' units?

Back

To translate a function down by 'k' units, you subtract 'k' from the function: f(x) becomes f(x) - k.

Front

How do you translate a function left by 'h' units?

Back

To translate a function left by 'h' units, you replace 'x' with 'x + h': f(x) becomes f(x + h).

Front

How do you translate a function right by 'h' units?

Back

To translate a function right by 'h' units, you replace 'x' with 'x - h': f(x) becomes f(x - h).

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you identify the vertex of the function f(x) = a(x - h)² + k?

Back

The vertex of the function f(x) = a(x - h)² + k is the point (h, k).