Exploring Transformations of Functions

The video introduces functions, emphasizing their importance in mathematics and real-life applications. It explains the vertical line test for identifying functions and discusses parent functions like constant, linear, absolute value, and quadratic functions. The video also covers transformations, including translations, stretches, shrinks, and reflections, and provides examples to illustrate these concepts.

What is the formal definition of a function?

• A relationship where outputs are always the same.

• A numerical relationship where inputs and outputs are the same.

• A numerical relationship where every input has exactly one output.

• A relationship where each input has multiple outputs.

Why is it important for a function to have a unique output for each input in real life?

• To allow for multiple solutions.

• To increase complexity.

• To make calculations easier.

• To ensure fairness and consistency.

What does the vertical line test determine?

• If a graph has multiple outputs.

• If a graph is symmetrical.

• If a graph is linear.

• If a graph represents a function.

Which of the following is a key feature of a constant function?

• It has a changing slope.

• It forms a U-shape.

• It is a horizontal line.

• It has a vertex at (0,0).

What is the parent function for a linear function?

• f(x) = x

• f(x) = c

• f(x) = |x|

• f(x) = x^2

What shape does the graph of an absolute value function form?

• A circle

• A V-shape

• A U-shape

• A straight line

Which transformation involves moving a graph left or right?

• Vertical translation

• Horizontal translation

• Reflection

• Vertical stretch

What happens when you multiply the entire function by a negative number?

• It stretches vertically.

• It shifts horizontally.

• It reflects over the Y-axis.

• It reflects over the X-axis.

In the transformation f(x) = 2|x + 3| - 1, what does the '+3' inside the absolute value indicate?

• A vertical shift down by 3 units

• A horizontal shift to the left by 3 units

• A horizontal shift to the right by 3 units

• A vertical stretch by a factor of 3

For the quadratic function f(x) = -3(x - 1)^2 + 5, what does the '-3' outside the parentheses indicate?

• A vertical stretch by a factor of 3

• A reflection over the Y-axis

• A horizontal shift to the right by 3 units

• A reflection over the X-axis