Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the process of changing the position, size, or shape of its graph through operations such as translation, reflection, stretching, or compression.

Front

What does reflecting a function over the y-axis do to its graph?

Back

Reflecting a function over the y-axis changes the sign of the x-coordinates of all points on the graph, resulting in a mirror image of the graph across the y-axis.

Front

How does shifting a function to the left affect its equation?

Back

Shifting a function to the left by 'h' units involves replacing 'x' with '(x + h)' in the function's equation.

Front

What is the effect of a vertical reflection on a function's graph?

Back

A vertical reflection flips the graph of the function over the x-axis, changing the sign of the function's output.

Front

What transformation is represented by the equation g(x) = f(x) + k?

Back

The equation g(x) = f(x) + k represents a vertical shift of the graph of f(x) upward by 'k' units if k > 0, and downward if k < 0.

Front

What does the transformation g(x) = f(x - h) represent?

Back

The transformation g(x) = f(x - h) represents a horizontal shift of the graph of f(x) to the right by 'h' units if h > 0, and to the left if h < 0.

Front

How do you denote a reflection of a function over the x-axis?

Back

A reflection of a function over the x-axis is denoted by g(x) = -f(x), which changes the sign of the output values.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x^2, which is the simplest form of a quadratic function.

Front

What does the transformation g(x) = f(-x) represent?

Back

The transformation g(x) = f(-x) represents a reflection of the graph of f(x) over the y-axis.

Front

What is the effect of a horizontal compression on a function's graph?

Back

A horizontal compression of a function's graph occurs when the input 'x' is multiplied by a factor greater than 1, resulting in a graph that is narrower.