Transformations and Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x²), and absolute value functions (y = |x|).

Front

What is the effect of shifting a graph to the right?

Back

Shifting a graph to the right involves adding a positive value to the x-variable in the function's equation. For example, y = |x - 5| represents the absolute value function shifted right by 5 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

Reflecting a graph over the x-axis changes the sign of the function. For example, y = x² becomes y = -x².

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the absolute value function?

Back

The absolute value function is defined as y = |x|, which outputs the non-negative value of x. Its graph forms a V-shape.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically involves adding or subtracting a constant from the function's output. For example, y = x² + 2 shifts the graph of y = x² up by 2 units.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines (y = mx + b), while quadratic functions have a variable rate of change and graph as parabolas (y = ax² + bx + c).

Front

What is a reflection in mathematics?

Back

A reflection is a transformation that flips a graph over a specified line, such as the x-axis or y-axis.

Front

What is the square root function?

Back

The square root function is defined as y = √x, which outputs the non-negative square root of x. Its graph is half of a parabola.