Transformations of Linear Equations

Front

What is a transformation of a linear equation?

Back

A transformation of a linear equation involves changing its position, slope, or shape on a graph without altering its linearity.

Front

What does the function g(x) = f(x - 6) represent?

Back

The function g(x) = f(x - 6) represents a horizontal shift of the graph of f(x) to the right by 6 units.

Front

What effect does the function g(x) = f(x) - 5 have on the graph of f(x)?

Back

The function g(x) = f(x) - 5 shifts the graph of f(x) down by 5 units.

Front

How does the slope of g(x) = f(x) - 5 compare to f(x)?

Back

The slope of g(x) = f(x) - 5 is the same as the slope of f(x).

Front

What is the y-intercept of the function g(x) = f(x) - 5 if the y-intercept of f(x) is 0?

Back

The y-intercept of g(x) = f(x) - 5 is -5.

Front

What does the function g(x) = 21f(x) indicate about the graph of f(x)?

Back

The function g(x) = 21f(x) indicates a vertical stretch of the graph of f(x) by a factor of 21.

Front

What is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x, which is a straight line through the origin with a slope of 1.

Front

What happens to the graph of f(x) when you add a positive number to it, like in g(x) = f(x) + 3?

Back

Adding a positive number shifts the graph of f(x) upward by that number of units.

Front

What happens to the graph of f(x) when you subtract a positive number from it, like in g(x) = f(x) - 2?

Back

Subtracting a positive number shifts the graph of f(x) downward by that number of units.

Front

If g(x) = f(x + 4), what is the effect on the graph of f(x)?

Back

The function g(x) = f(x + 4) represents a horizontal shift of the graph of f(x) to the left by 4 units.