Transformations of Functions (alg 2)

Front

What is a transformation of a function?

Back

A transformation of a function is a change made to the function's graph, which can include translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function up or down?

Back

Translating a function up means adding a constant to the function's output, while translating it down means subtracting a constant from the output.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + 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 is the highest or lowest point of the parabola, depending on the direction it opens.

Front

What is the effect of adding a constant to the function f(x)?

Back

Adding a constant to f(x) translates the graph vertically. For example, f(x) + k moves the graph up by k units.

Front

What is the effect of subtracting a constant from the function f(x)?

Back

Subtracting a constant from f(x) translates the graph vertically down. For example, f(x) - k moves the graph down by k units.

Front

What does the notation f(x - h) represent?

Back

The notation f(x - h) represents a horizontal translation of the graph to the right by h units.

Front

What does the notation f(x + h) represent?

Back

The notation f(x + h) represents a horizontal translation of the graph to the left by h units.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis occurs when the output of the function is multiplied by -1, resulting in f(x) = -f(x).