Precalculus: Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean to shift a function to the right?

Back

Shifting a function to the right means adding a positive value to the x-variable in the function's equation, which moves the graph horizontally to the right.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

How does reflecting a function over the x-axis affect its graph?

Back

Reflecting a function over the x-axis changes the sign of the output values, flipping the graph upside down.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x², which is a parabola that opens upwards.

Front

What does the notation f(x) = (x - h)² + k represent?

Back

This notation represents a quadratic function that has been transformed, where (h, k) is the vertex of the parabola.

Front

What is the effect of a horizontal shift on a function?

Back

A horizontal shift occurs when a constant is added or subtracted from the x-variable, moving the graph left or right.

Front

What does a negative sign in front of a function indicate?

Back

A negative sign in front of a function indicates a reflection over the x-axis.

Front

What is the transformation of f(x) = x² to g(x) = x² - 5?

Back

The transformation is a vertical shift downward by 5 units.

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

In vertex form, f(x) = a(x - h)² + k, the vertex is the point (h, k).