Understanding Functions and Their Properties

The video tutorial explains how to determine which function has a greater Y-intercept by evaluating the Y-coordinate when X equals zero. It compares two functions, F(x) and G(x), and identifies their Y-intercepts. The tutorial then explores how to find common roots between functions by factoring and analyzing their equations. Finally, it discusses concavity, explaining how the sign of the coefficient of the squared term in a quadratic function determines whether the graph is concave upwards or downwards.

What is the Y-intercept of the function f(x)?

• 5

• 4

• 3

• 2

Which function has a greater Y-intercept?

• f(x)

• g(x)

• Both have the same

• Cannot be determined

How many roots does the function g(x) have?

• 4

• 2

• 1

• 3

What are the roots of the function g(x)?

• x = 0 and x = 3

• x = 1 and x = -2

• x = -3 and x = 2

• x = -1 and x = 2

How many roots do the functions f(x) and g(x) have in common?

• 3

• 2

• 1

• 0

What is the concavity of the function g(x)?

• Cannot be determined

• Linear

• Concave downwards

• Concave upwards

What determines the concavity of a quadratic function?

• The y-intercept

• The constant term

• The coefficient of x

• The coefficient of x^2

If the coefficient of x^2 is positive, what is the concavity of the function?

• Cannot be determined

• Concave upwards

• Concave downwards

• Linear

Do the functions f(x) and g(x) have the same concavity?

• Cannot be determined

• Yes

• No

• Only at the vertex

If a function is concave downwards, what can be said about its coefficient of x^2?

• It is positive

• It is negative

• It is zero

• It is undefined