Parent Function Translations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions in the same family are derived by transformations such as translations, reflections, and stretches.

Front

What does a vertical translation of a function do?

Back

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

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function's output (f(x) + k) translates the graph vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What does a horizontal translation of a function do?

Back

A horizontal translation shifts the graph of the function left or right without changing its shape.

Front

How does subtracting a constant from the input of a function affect its graph?

Back

Subtracting a constant from the input (f(x - h)) translates the graph horizontally to the right by h units; if h is negative, it shifts left.

Front

What is the effect of the transformation g(x) = f(x) + k?

Back

The transformation g(x) = f(x) + k shifts the graph of f(x) vertically by k units.

Front

What is the effect of the transformation g(x) = f(x - h)?

Back

The transformation g(x) = f(x - h) shifts the graph of f(x) horizontally to the right by h units.

Front

What does the equation y = x^2 + 5 represent?

Back

The equation y = x^2 + 5 represents a quadratic function that has been translated vertically up 5 units from the parent function y = x^2.

Front

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

Back

The equation y = (x + 4)^2 represents a quadratic function that has been translated horizontally left 4 units from the parent function y = x^2.

Front

What is the general form of a quadratic function?

Back

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