Transforming Functions

Front

What is a transformation in the context of functions?

Back

A transformation is an operation that alters the form of a function's graph, including shifts, reflections, stretches, and compressions.

Front

What does a negative sign in front of a function indicate?

Back

It indicates a reflection of the graph over the x-axis.

Front

What does a positive value less than 1 (e.g., ⅔) indicate in a transformation?

Back

It indicates a vertical compression of the graph by that factor.

Front

How do you translate a function to the right?

Back

To translate a function to the right, you subtract from the x-value in the function's equation (e.g., f(x - h) translates right by h units).

Front

How do you translate a function to the left?

Back

To translate a function to the left, you add to the x-value in the function's equation (e.g., f(x + h) translates left by h units).

Front

What does the equation f(x) = (x - 4)^2 + 7 represent?

Back

It represents a function that is translated 4 units to the right and 7 units up from the parent function f(x) = x^2.

Front

What is the effect of a vertical stretch by a factor of 2 on a function?

Back

It multiplies the output of the function by 2, making the graph steeper.

Front

What does the equation y = -√(x + 4) + 9 indicate about the transformations?

Back

It indicates a reflection over the x-axis, a shift 4 units left, and a shift 9 units up.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2.

Front

How do you identify a reflection over the y-axis in a function?

Back

A reflection over the y-axis occurs when the function is replaced with f(-x).