Review: 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 is the parent function of linear functions?

Back

Front

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

Back

The transformation g(x) = -f(x) reflects the graph of f(x) across the x-axis.

Front

What effect does the transformation g(x) = f(x) - 3 have on the graph of f(x)?

Back

The transformation g(x) = f(x) - 3 translates the graph of f(x) down by 3 units.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the graph.

Front

How does the transformation g(x) = 4f(x) affect the steepness of the graph?

Back

The transformation g(x) = 4f(x) makes the graph steeper by a factor of 4.

Front

What is the effect of the transformation g(x) = (1/4)f(x)?

Back

The transformation g(x) = (1/4)f(x) compresses the graph vertically by a factor of 1/4.

Front

What does the term 'reflection' mean in the context of linear transformations?

Back

Reflection in linear transformations refers to flipping the graph over a specific axis, such as the x-axis or y-axis.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of the function when x = 0.

Front

What does it mean for a function to be 'steeper'?

Back

A function is considered 'steeper' if it has a larger absolute value of the slope, indicating a greater change in y for a given change in x.