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 a linear equation?

Back

The parent function of a linear equation is y = x, which represents a straight line through the origin with a slope of 1.

Front

How does the graph of y = mx + b differ from the parent function?

Back

The graph of y = mx + b is a linear function where 'm' represents the slope and 'b' represents the y-intercept, shifting the graph vertically.

Front

What effect does multiplying a function by a scalar have on its graph?

Back

Multiplying a function by a scalar compresses or stretches the graph vertically, depending on whether the scalar is between 0 and 1 (compression) or greater than 1 (stretching).

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down along the y-axis without changing its shape.

Front

What is the transformation of the function f(x) = x when it becomes g(x) = f(x) + c?

Back

The transformation shifts the graph of f(x) vertically by 'c' units; if c is positive, it shifts up, and if c is negative, it shifts down.

Front

What is the effect of a negative slope in a linear function?

Back

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

Front

How do you describe a transformation that makes a graph steeper?

Back

A transformation that makes a graph steeper involves increasing the absolute value of the slope 'm' in the equation y = mx + b.

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, indicating the value of the function when x = 0.

Front

How does adding a constant to a linear function affect its graph?

Back

Adding a constant to a linear function shifts the graph vertically by that constant value.