Unit 4: Transformation of Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which can be transformed to create other functions.

Front

What does it mean to translate a graph?

Back

To translate a graph means to shift it horizontally and/or vertically without changing its shape.

Front

What is the effect of a reflection over the x-axis on a function?

Back

A reflection over the x-axis flips the graph of the function upside down.

Front

What is the effect of a reflection over the y-axis on a function?

Back

A reflection over the y-axis flips the graph of the function horizontally.

Front

How do you determine the vertex of a parabola in vertex form?

Back

The vertex of a parabola in the form y = a(x-h)² + k is (h, k).

Front

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

Back

The domain of y = √(x) is [0, ∞) because the square root is only defined for non-negative values.

Front

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

Back

The range of y = √(x) is [0, ∞) because the output values (y) are also non-negative.

Front

What does the notation f(x) = -|x| + 2 represent?

Back

This represents a vertical reflection of the absolute value function, shifted up by 2 units.

Front

What transformation is represented by the function f(x) = |x| - 2?

Back

This function represents a vertical translation of the absolute value function down by 2 units.

Front

What is the transformation of the function y = 2(x-3)² + 4 compared to y = x²?

Back

This function is a vertical stretch by a factor of 2, translated right 3 units, and up 4 units.