Graphing and Analyzing Functions

The video tutorial revisits the concept of graphs, using a musical metaphor to explain their representation. It covers linear graphs, including horizontal and vertical lines, and discusses gradients. The tutorial then introduces parabolas and their transformations, followed by an exploration of cubic functions and sideways parabolas.

What metaphor is used to explain the relationship between equations and graphs?

• Graphs are like paintings.

• Graphs are like stories.

• Graphs are like puzzles.

• Graphs are like musical notes.

What is the shape of the graph for the equation y = x?

• A circular line

• A curved line

• A straight line

• A zigzag line

How do you change the direction of a linear graph from positive to negative?

• By adding a constant

• By multiplying by a negative number

• By swapping x and y

• By rotating the graph

What is the equation of a horizontal line?

• y = constant

• x = constant

• x = y

• y = x

What is the gradient of a vertical line?

• Undefined

• One

• Zero

• Negative

What happens to the gradient when a line is horizontal?

• It becomes zero

• It becomes one

• It becomes negative

• It becomes undefined

What is the shape of the graph for the equation y = x^2?

• A straight line

• A parabola

• A cubic curve

• A circle

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

• It is the same

• It is upside down

• It is narrower

• It is wider

What is the result of swapping x and y in the equation y = x^2?

• A cubic curve

• A sideways parabola

• A horizontal line

• A vertical line

What is the shape of a cubic function graph?

• A straight line

• A parabola

• A cubic curve

• A circle