24-25 Alg1 3-7 FLASHCARD - Linear Transformations

Front

What is a linear transformation?

Back

A linear transformation is a function that maps a vector space to another vector space, preserving the operations of vector addition and scalar multiplication.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x.

Front

How does shifting a function vertically affect its equation?

Back

Shifting a function vertically by 'k' units results in the new function being f(x) + k.

Front

What does it mean to compress a function horizontally by a factor of 'a'?

Back

Compressing a function horizontally by a factor of 'a' means the new function is f(ax), where 'a' is greater than 1.

Front

Describe the transformation represented by g(x) = f(x + 6).

Back

The transformation g(x) = f(x + 6) represents a shift of the graph of f left by 6 units.

Front

What is the effect of reflecting a graph over the x-axis?

Back

Reflecting a graph over the x-axis changes the sign of the output values, resulting in the function -f(x).

Front

If a function is vertically stretched by a factor of 'b', what is the new function?

Back

The new function after a vertical stretch by a factor of 'b' is b * f(x).

Front

What does the transformation g(x) = f(3x) represent?

Back

The transformation g(x) = f(3x) represents a horizontal compression of the graph of f by a factor of 3.

Front

How do you describe a vertical shift of a function?

Back

A vertical shift of a function is described by adding or subtracting a constant from the function's output.

Front

What is the result of a horizontal shift to the right by 'c' units?

Back

A horizontal shift to the right by 'c' units results in the new function f(x - c).