Transformations of Parent Functions

Front

What is a square root function?

Back

A square root function is a function of the form y = √x, which represents the principal square root of x. It is defined for x ≥ 0 and has a graph that starts at the origin and increases gradually.

Front

What is an absolute value function?

Back

An absolute value function is a function of the form y = |x|, which outputs the non-negative value of x. Its graph forms a V shape, opening upwards.

Front

What does it mean to shift a graph right 5 units?

Back

Shifting a graph right 5 units means to replace x with (x - 5) in the function's equation, moving every point on the graph 5 units to the right.

Front

What is the transformation of y = |x| to y = |x - 5|?

Back

The transformation is a horizontal shift to the right by 5 units.

Front

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

Back

Reflecting a graph over the x-axis means to multiply the function by -1, which flips the graph upside down.

Front

What is a vertical stretch in graph transformations?

Back

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

Front

What is a vertical compression in graph transformations?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

How does the graph of y = -2|x| differ from y = |x|?

Back

The graph of y = -2|x| is a vertical stretch of the absolute value function reflected over the x-axis.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x², which is a parabola opening upwards.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function translates the graph vertically. For example, y = f(x) + c shifts the graph up by c units.