Transformation of functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, including shifts, stretches, compressions, and reflections.

Front

What does a right shift of a function mean?

Back

A right shift of a function means that the graph of the function moves to the right along the x-axis by a certain number of units.

Front

What does an upward shift of a function mean?

Back

An upward shift of a function means that the graph of the function moves up along the y-axis by a certain number of units.

Front

What is the general form of a quadratic function?

Back

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

Front

How does the value of 'a' affect the graph of a quadratic function?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does it mean for a function to have a range of [0, ∞)?

Back

A range of [0, ∞) means that the function's output values start at 0 and extend to positive infinity, indicating that the function does not produce negative values.

Front

What is the effect of subtracting a constant from a function?

Back

Subtracting a constant from a function results in a downward shift of the graph by that constant value.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function results in an upward shift of the graph by that constant value.