Transformations of Linear Functions

Front

What is a translation in the context of linear functions?

Back

A translation is a shift of a graph in the coordinate plane without changing its shape or orientation.

Front

How does the function g(x) = f(x) - 2 transform f(x)?

Back

It translates the graph of f(x) down by 2 units.

Front

What effect does g(x) = f(x + 1) have on the graph of f(x)?

Back

It translates the graph of f(x) left by 1 unit.

Front

If g(x) = f(x) + 5, how does this affect the graph of f(x)?

Back

It translates the graph of f(x) up by 5 units.

Front

What does g(x) = f(x - 1) do to the graph of f(x)?

Back

It translates the graph of f(x) right by 1 unit.

Front

What is the result of t(x) = f(x + 3) + 5 in terms of translations?

Back

It translates the graph of f(x) left by 3 units and up by 5 units.

Front

What is the general form of a linear function?

Back

The general form is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope represents the rate of change of the function, indicating how steep the line is.

Front

What does the y-intercept (b) indicate in a linear function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of f(x) when x = 0.

Front

How do you identify a vertical translation from a function?

Back

A vertical translation occurs when a constant is added or subtracted from the function, affecting the y-values.