Graphing Polynomial and Rational Functions

This video tutorial explores various proportionality graphs, including direct proportionality to x, x squared, x cubed, and the square root of x, as well as inverse proportionality to x. It explains how to replace the proportionality sign with an equation involving a constant of proportionality and illustrates each concept with corresponding graphs. The video also provides examples and insights into the behavior of these graphs as the variables change.

What is the main focus of the video?

• Statistics

• Geometry

• Proportionality graphs

• Algebraic equations

Which of the following is a characteristic of a graph where y is directly proportional to x?

• It is a vertical line.

• It is a horizontal line.

• It forms a parabola.

• It passes through the origin.

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

• The line becomes less steep.

• The line becomes steeper.

• The line becomes a curve.

• The line shifts downwards.

What is the effect of increasing k in the graph of y = kx?

• The line becomes a curve

• The line shifts downwards

• The line becomes steeper

• The line becomes less steep

In an inverse proportionality graph, what happens to y as x increases?

• y decreases.

• y becomes zero.

• y remains constant.

• y increases.

What type of graph represents y = k/x?

• Reciprocal graph

• Parabola

• Linear graph

• Exponential graph

If y = 20/x, what is the value of y when x = 5?

• 4

• 5

• 20

• 10

In the graph of y = k/x, what happens to y as x decreases?

• y becomes zero

• y increases

• y remains constant

• y decreases

What is the value of y when x = 10 in the equation y = 20/x?

• 0.5

• 10

• 2

• 20

What shape does the graph of y = kx² take?

• A hyperbola

• A circle

• A parabola

• A straight line