12.17.24 Transformation of Functions

Front

What is a reflection across the x-axis in a function?

Back

A reflection across the x-axis occurs when the output values of a function are negated. For example, if the original function is f(x), the reflected function is -f(x).

Front

How do you shift a function downward by 2 units?

Back

To shift a function downward by 2 units, subtract 2 from the function. For example, if f(x) is the original function, the new function will be f(x) - 2.

Front

What does it mean to shift a function to the right by 3 units?

Back

Shifting a function to the right by 3 units means replacing x with (x - 3) in the function. For example, if f(x) is the original function, the new function will be f(x - 3).

Front

What is the parent function of a quadratic equation?

Back

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

Front

How does the graph of f(x) = x^2 + 5 differ from the parent function?

Back

The graph of f(x) = x^2 + 5 is the same as the parent function but shifted vertically upward by 5 units.

Front

What transformation does g(x) = (x - 3)^2 represent compared to f(x) = x^2?

Back

The transformation g(x) = (x - 3)^2 represents a horizontal shift to the right by 3 units compared to the parent function f(x) = x^2.

Front

What is the effect of a negative sign in front of a function, such as in f(x) = -x^2?

Back

A negative sign in front of a function reflects the graph across the x-axis. For example, f(x) = -x^2 is a downward-opening parabola.

Front

How do you represent a vertical shift of a function?

Back

A vertical shift of a function is represented by adding or subtracting a constant from the function. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What does the notation f(x) = (x + 3)^2 indicate about the graph?

Back

The notation f(x) = (x + 3)^2 indicates that the graph of the function is shifted to the left by 3 units compared to the parent function f(x) = x^2.

Front

What is the transformation of f(x) = x^2 - 2 compared to the parent function?

Back

The transformation of f(x) = x^2 - 2 compared to the parent function is a vertical shift downward by 2 units.