Translations of Functions

Front

What is a translation of a function?

Back

A translation of a function is a shift of the graph of the function in a specific direction without changing its shape.

Front

How does the equation y = (x + 4)² represent a translation?

Back

It represents a translation of the graph of y = x² to the left by 4 units.

Front

What does the equation y = x² + 5 indicate about the graph?

Back

It indicates that the graph of y = x² is translated upward by 5 units.

Front

Describe the transformation represented by g(x) = f(x + 5).

Back

The graph of f(x) is translated to the left by 5 units.

Front

What does the transformation g(x) = f(x - 3) do to the graph?

Back

The graph of f(x) is translated to the right by 3 units.

Front

If a function is translated down 4 units, how is its equation affected?

Back

The equation is modified by subtracting 4 from the output, e.g., y = f(x) becomes y = f(x) - 4.

Front

What is the effect of translating a function right by 2 units?

Back

The equation changes by replacing x with (x - 2), e.g., y = f(x) becomes y = f(x - 2).

Front

How do you identify a left translation in a function's equation?

Back

A left translation is identified when the equation has (x + k) where k > 0, indicating a shift left.

Front

What does the term 'vertical translation' refer to?

Back

Vertical translation refers to shifting the graph of a function up or down along the y-axis.

Front

What is the general form of a quadratic function?

Back

The general form is y = ax² + bx + c, where a, b, and c are constants.