Transformations 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, including shifts, reflections, stretches, and compressions.

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 input variable (x) in the function, resulting in a horizontal translation.

Front

What is the effect of subtracting a value from the input of a function?

Back

Subtracting a value from the input of a function shifts the graph to the right by that value.

Front

How does reflecting a graph over the x-axis affect its equation?

Back

Reflecting a graph over the x-axis changes the sign of the output (y-values) in the function's equation.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient 'a' in the equation f(x) = ax² + bx + c is positive.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient 'a' in the equation f(x) = ax² + bx + c is negative.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you translate a graph downwards?

Back

To translate a graph downwards, you subtract a positive value from the output (y) in the function's equation.

Front

What is the effect of adding a value to the output of a function?

Back

Adding a value to the output of a function shifts the graph vertically upwards.