Transformations of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope (m) of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept (b) of a linear function is the point where the graph of the function crosses the y-axis. It represents the value of f(x) when x = 0.

Front

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

Back

The graph of g(x) = f(x) + c is a vertical shift of the graph of f(x) by c units. If c is positive, the graph shifts up; if c is negative, it shifts down.

Front

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

Back

Multiplying a function by a constant (g(x) = kf(x)) stretches or compresses the graph vertically. If k > 1, the graph stretches; if 0 < k < 1, it compresses.

Front

What is the transformation represented by g(x) = f(x) - 4?

Back

The transformation g(x) = f(x) - 4 represents a vertical shift of the graph of f(x) downwards by 4 units.

Front

What does g(x) = 3f(x) indicate about the graph of f(x)?

Back

The equation g(x) = 3f(x) indicates that the graph of f(x) is stretched vertically by a factor of 3.

Front

What is the transformation represented by g(x) = 1/3f(x)?

Back

The transformation g(x) = 1/3f(x) compresses the graph of f(x) vertically by a factor of 1/3.

Front

How do you identify a vertical shift in a linear function?

Back

A vertical shift in a linear function can be identified by the addition or subtraction of a constant to the function, such as g(x) = f(x) + c.

Front

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

Back

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