Parent Functions and Transformations

Questions and Answers

What is the definition of the Linear (Parent) Function?

f(x) = x (correct)

f(x) = a|x-h| + k

f(x) = |x|

f(x) = -f(x)

What is the definition of the Absolute Value (Parent) Function?

f(x) = |x| (correct)

f(x) = a|x-h| + k

f(x) = x

f(x) = -f(x)

What is the Vertex Form of an Absolute Value Function?

a | x-h | + k

What does 'a' represent in the Vertex Form?

slope on the right side, -a = slope on the left side Signup and view all the answers

What is the Vertex in Vertex Form?

(h,k) Signup and view all the answers

What does f(x+h) represent?

transformation to shift to the LEFT 'h' units Signup and view all the answers

What does f(x-h) represent?

transformation to shift to the RIGHT 'h' units Signup and view all the answers

What does f(x)+k represent?

transformation to shift UP 'k' units Signup and view all the answers

What does f(x)-k represent?

transformation to shift DOWN 'k' units Signup and view all the answers

What does it mean when a function is skinnier/vertical stretch?

a f(x) WHEN | a | > 1 Signup and view all the answers

What does it mean when a function is wider/horizontal stretch?

a f(x) WHEN | a | < 1 Signup and view all the answers

What is the transformation for reflection/flip over the x-axis?

-f(x) Signup and view all the answers

Study Notes

Parent Functions

Linear Function: Defined as f(x) = x or y = x. It represents a straight line with a constant slope.
Absolute Value Function: Represented as f(x) = |x| or y = |x|. Forms a V shape on the graph, reflecting all negative values above the x-axis.

Vertex Form of Absolute Value Function

General Form: a |x - h| + k, where (h,k) indicates the vertex of the function.

Characteristics of Vertex Form

Slope: The slope of the right side of the vertex is a, while the left side slope is -a.
Vertex: Given by the coordinates (h, k), the vertex is the point at which the graph changes direction.

Transformations of Functions

Shift Left: The transformation f(x + h) shifts the graph to the left by 'h' units.
Shift Right: The transformation f(x - h) shifts the graph to the right by 'h' units.
Shift Up: The transformation f(x) + k shifts the graph upward by 'k' units.
Shift Down: The transformation f(x) - k shifts the graph downward by 'k' units.

Dilation

Vertical Stretch: Occurs when a > 1, resulting in a skinnier graph.
Vertical Compression: Occurs when 0 < |a| < 1, leading to a wider graph.

Reflections

Reflection over x-axis: Represented by -f(x), this transformation flips the graph over the x-axis.

Description

Test your understanding of parent functions such as linear and absolute value functions. Explore the characteristics of the vertex form and learn about transformations including shifting graphs. This quiz will help reinforce your knowledge of key concepts in mathematics.