4.07 Linear Transformations Review

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What does the function f(x) = 3x represent?

Back

It represents a linear function with a slope of 3, indicating that for every unit increase in x, f(x) increases by 3.

Front

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

Back

Shifting a function to the right by 2 units means that every point on the graph of the function moves 2 units to the right along the x-axis.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does dilation mean in the context of transformations?

Back

Dilation refers to a transformation that alters the size of a figure but not its shape, typically by a scale factor.

Front

How do you represent a function that is a translation of another function?

Back

A function g(x) that is a translation of f(x) can be represented as g(x) = f(x - h) + k, where h and k are the horizontal and vertical shifts, respectively.

Front

What is the transformation when g(x) = f(x - 2)?

Back

The transformation is a translation of the function f(x) to the right by 2 units.

Front

What is the slope of the function h(x) = 4x + 1?

Back

The slope of the function h(x) = 4x + 1 is 4.

Front

What does it mean if a function is reflected over the x-axis?

Back

If a function is reflected over the x-axis, all y-values of the function are multiplied by -1, resulting in a vertical flip of the graph.

Front

What is the difference between a translation and a dilation?

Back

A translation shifts a graph without changing its shape or size, while a dilation changes the size of the graph but keeps its shape.