Linear Transformations Flashcard

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 slope of a line represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What effect does a positive vertical shift have on a linear function?

Back

A positive vertical shift moves the graph of the function upward by a specified number of units.

Front

What effect does a negative vertical shift have on a linear function?

Back

A negative vertical shift moves the graph of the function downward by a specified number of units.

Front

How does doubling the slope of a linear function affect its graph?

Back

Doubling the slope makes the line steeper, meaning it rises or falls more quickly as x changes.

Front

What is the parent function of a linear equation?

Back

The parent function of a linear equation is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What happens to the graph of a linear function when the slope is halved?

Back

Halving the slope makes the line less steep, meaning it rises or falls more slowly as x changes.

Front

What does it mean for a line to be 'less steep' than another?

Back

A line is 'less steep' if it has a smaller absolute value of slope compared to another line.

Front

How do you represent a linear function that has been shifted up by 3 units?

Back

To shift a linear function f(x) = mx + b up by 3 units, the new function is f(x) = mx + (b + 3).

Front

What is the effect of a horizontal shift on a linear function?

Back

A horizontal shift moves the graph of the function left or right, depending on whether the shift is negative or positive.