24-25 Alg1 3-7 FLASHCARD - Linear Transformations

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 it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down on the coordinate plane without changing its shape.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

Multiplying a function by a factor greater than 1 vertically stretches the graph away from the x-axis.

Front

What is the effect of multiplying a function by a factor between 0 and 1?

Back

Multiplying a function by a factor between 0 and 1 vertically compresses the graph towards the x-axis.

Front

What does the notation g(x) = f(x) + k represent?

Back

This notation represents a vertical shift of the graph of f(x) by k units; if k is positive, the graph shifts up, and if k is negative, it shifts down.

Front

What does the notation g(x) = f(kx) represent?

Back

This notation represents a horizontal transformation; if k > 1, the graph compresses horizontally, and if 0 < k < 1, it stretches horizontally.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which is a straight line through the origin with a slope of 1.

Front

How does the graph of g(x) = -f(x) differ from f(x)?

Back

The graph of g(x) = -f(x) is a reflection of f(x) across the x-axis.

Front

What does it mean to compress a graph horizontally?

Back

Compressing a graph horizontally means to make it narrower, which occurs when the input variable x is multiplied by a factor greater than 1.

Front

What is the transformation represented by g(x) = f(x - h)?

Back

This represents a horizontal shift to the right by h units; if h is negative, it shifts to the left.