Graph Behavior of y = 1/x²

In this video, Dr. B demonstrates how to graph the function y = 1/x² by starting with the graph and working backwards. The video explores graphing with negative, fractional, and positive x values, showing how the graph is symmetrical across the y-axis. The tutorial explains that squaring negative values results in positive y values, and how fractional values affect the graph. The video concludes with a mirrored graph for positive x values, reinforcing the concept of symmetry in the function's graph.

What is the general shape of the graph of y = 1/x²?

• A straight line

• A hyperbola

• A parabola

• A circle

When x is -1, what is the value of y in the graph of y = 1/x²?

• 0

• 2

• 1

• -1

For x = -2, what is the corresponding y value on the graph of y = 1/x²?

• 1/16

• 1/8

• 1/4

• 1/2

What happens to the y value as x becomes more negative in the graph of y = 1/x²?

• y remains constant

• y becomes larger

• y approaches zero

• y becomes negative

What is the y value when x is -1/2 in the graph of y = 1/x²?

• 2

• 1

• 4

• 3

How does the graph of y = 1/x² behave when x is a small negative fraction?

• y becomes very large

• y becomes very small

• y becomes negative

• y becomes zero

What is the y value when x is 2 in the graph of y = 1/x²?

• 1/8

• 1/4

• 1/16

• 1/2

How does the graph of y = 1/x² for positive x values compare to negative x values?

• It is a mirror image

• It is completely different

• It is identical

• It is shifted upwards

What is the effect of squaring x in the equation y = 1/x²?

• It makes y zero

• It has no effect

• It makes y positive

• It makes y negative

What is the general behavior of the graph of y = 1/x² as x approaches zero?

• y approaches infinity

• y approaches zero

• y remains constant

• y becomes negative