Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the x-variable in the function, resulting in the entire graph moving horizontally to the right.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the new point will be (x, -y), effectively flipping the graph upside down.

Front

What is the effect of subtracting a constant from a function, y = f(x) - c?

Back

Subtracting a constant c from a function shifts the graph downward by c units.

Front

What is the effect of adding a constant to the x-variable, y = f(x + c)?

Back

Adding a constant c to the x-variable shifts the graph to the left by c units.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a horizontal compression of a function?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, making the graph narrower.

Front

What is the parent function of y = √(x)?

Back

The parent function of y = √(x) is the basic square root function, which has a domain of x ≥ 0 and a range of y ≥ 0.

Front

How does the function g(x) = (x - 1)³ transform the parent function f(x) = x³?

Back

The function g(x) = (x - 1)³ shifts the graph of the parent function f(x) = x³ to the right by 1 unit.

Front

What is the transformation of y = f(1/5x)?

Back

The transformation of y = f(1/5x) is a horizontal stretch by a factor of 5.