PreCalc- All Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to translate a function up?

Back

Translating a function up means adding a constant to the function's output, shifting the graph vertically upwards.

Front

How does the equation y = x² + 5 represent a transformation?

Back

This equation represents a vertical translation of the basic quadratic function y = x², shifted up 5 units.

Front

What is a horizontal stretch of a function?

Back

A horizontal stretch occurs when the input of the function is multiplied by a factor less than 1, making the graph wider.

Front

What does the transformation y = f(1/5x) indicate?

Back

This transformation indicates a horizontal stretch by a factor of 5.

Front

How do you translate a function left?

Back

To translate a function left, you subtract a constant from the input variable, shifting the graph horizontally to the left.

Front

What does the equation y = (x + 4)² represent?

Back

This equation represents a quadratic function translated left 4 units from the basic function y = x².

Front

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

Back

Reflecting a function over the x-axis means multiplying the output by -1, flipping the graph upside down.

Front

How does the equation y = -x² + 2 represent transformations?

Back

This equation represents a reflection over the x-axis and a vertical translation up 2 units.

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input, typically in the form y = |x|.