Proportionality and Graph Behavior

This video tutorial covers various types of proportionality graphs, including direct proportionality to x, inverse proportionality to x, direct proportionality to x squared, x cubed, and the square root of x. Each section explains how to replace the proportionality sign with an equation involving a constant, and how the graph of each relationship looks. The video emphasizes understanding the shape and behavior of these graphs, such as diagonal lines, reciprocal graphs, parabolas, cubic curves, and square root curves, and how the constant affects the steepness of the graph.

What is the primary focus of the video on proportionality graphs?

• Studying trigonometric functions

• Understanding the concept of direct and inverse proportions

• Learning about linear equations

• Exploring quadratic equations

When y is directly proportional to x, what does the graph look like?

• A diagonal line through the origin

• A vertical line

• A horizontal line

• A parabola

In the context of the video, what does the constant k represent?

• The slope of the line

• The y-intercept

• The constant of proportionality

• The x-intercept

In a graph where y is inversely proportional to x, what happens to y as x increases?

• y remains constant

• y decreases

• y oscillates

• y increases

What type of graph is formed when y is inversely proportional to x?

• Parabolic graph

• Exponential graph

• Linear graph

• Reciprocal graph

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

• It is a straight line

• It is a parabola

• It is a horizontal line

• It is a vertical line

What shape does the graph of y = kx^3 take?

• A circle

• A parabola

• A straight line

• A cubic curve

What happens to the graph of y = kx^2 as the value of k increases?

• It shifts upwards

• It shifts downwards

• It becomes shallower

• It becomes steeper

What is the starting point of the graph for y = k√x?

• At (1,1)

• At (0,0)

• At (1,0)

• At (0,1)

Which graph represents y being directly proportional to the square root of x?

• A cubic curve

• A straight line

• A parabola

• A square root curve