Transformations of Functions (x^2, x^3, |x|, √x)

Front

What is a transformation of a function?

Back

A transformation of a function refers to the process of changing its position, shape, or size on a graph, which can include translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function vertically?

Back

Translating a function vertically involves shifting the graph up or down by adding or subtracting a constant from the function's output.

Front

What is the effect of the transformation f(x) = -|x| + 2 on the graph of f(x) = |x|?

Back

This transformation reflects the graph of f(x) = |x| over the x-axis and then translates it upward by 2 units.

Front

How do you identify the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce, determined by analyzing the function's graph or algebraic expression.

Front

What is the range of the function f(x) = -|x| + 2?

Back

The range of f(x) = -|x| + 2 is (-∞, 2], as the maximum value occurs at y = 2 when x = 0.

Front

What does the notation f(x) = -(x + 2)^3 - 1 represent?

Back

This notation represents a transformation of the cubic function f(x) = x^3, which is reflected over the x-axis, translated left by 2 units, and translated down by 1 unit.

Front

What is the effect of the transformation g(x) = (x - 3)^2 on the function f(x) = x^2?

Back

The transformation g(x) = (x - 3)^2 translates the graph of f(x) = x^2 to the right by 3 units.

Front

What does the transformation g(x) = -f(x) indicate about the function f(x)?

Back

The transformation g(x) = -f(x) indicates that the graph of f(x) has been reflected over the x-axis.

Front

What is a reflection in the context of function transformations?

Back

A reflection is a transformation that flips a graph over a specified axis, such as the x-axis or y-axis.

Front

How does a vertical stretch affect the graph of a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph appear taller.