Transformation of Functions

Front

What is the effect of multiplying a function by -1 (e.g., y = -f(x))?

Back

The graph of the function is reflected over the x-axis.

Front

What does it mean to shift a graph to the right by a certain number of units?

Back

To shift a graph to the right by 'h' units, replace x with (x - h) in the function.

Front

What is the transformation when a function is reflected over the y-axis?

Back

The transformation is represented by y = f(-x).

Front

How does a vertical stretch affect the graph of a function?

Back

A vertical stretch by a factor of 'a' (where a > 1) multiplies the output of the function, making the graph taller.

Front

What is the transformation represented by y = f(x) + k?

Back

The graph of the function is shifted vertically by 'k' units; if k is positive, it shifts up, and if negative, it shifts down.

Front

What does a horizontal stretch by a factor of 'b' (where b > 1) do to the graph of a function?

Back

It stretches the graph away from the y-axis, making it wider.

Front

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

Back

The parent function is the square root function, which is defined for x ≥ 0.

Front

How do you represent a vertical shift of a function downwards?

Back

A vertical shift downwards by 'k' units is represented by y = f(x) - k.

Front

What is the transformation when a function is shifted left by 'h' units?

Back

To shift a graph left by 'h' units, replace x with (x + h) in the function.

Front

What does the transformation y = f(1/5x) indicate?

Back

This indicates a horizontal stretch by a factor of 5.