Transformation : Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions can be derived by transformations.

Front

What transformation occurs when a function is reflected over the y-axis?

Back

The transformation results in the function being mirrored across the y-axis, changing the sign of the x-values.

Front

What is the effect of translating a function to the right by 1 unit?

Back

The entire graph of the function shifts to the right by 1 unit, affecting the x-values of the function.

Front

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

Back

Reflecting a function over the x-axis means that the y-values of the function are multiplied by -1, resulting in a vertical flip.

Front

How do you denote the transformation of a function g(x) = f(x - 1) - 5?

Back

This denotes a translation of the function f(x) to the right by 1 unit and down by 5 units.

Front

What are the x-intercepts of a function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, corresponding to the values of x for which f(x) = 0.

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

Front

What does the transformation g(x) = (x - 1)^3 represent?

Back

This transformation represents a horizontal shift of the parent cubic function f(x) = x^3 to the right by 1 unit.

Front

What is the significance of zeros in a quadratic equation?

Back

Zeros are the values of x that make the quadratic equation equal to zero, indicating the x-intercepts of the graph.

Front

How does a vertical translation affect a function?

Back

A vertical translation shifts the graph of the function up or down without changing its shape.