Analyzing Graphs of Functions

• y =  ^_(x + 2)(x - 1)²
• y = -(x - 2)(x + 1)²
• y = (x - 2)(x + 1)²
• y = -x³

identify zeros

• (-1,0)

• (0,-1)

• (-0.333,1.333)

• (0.333,0)

How many zeros can this function have?

• only 1

• must have 2

• 1-2

• 0-2

Does (-1,0) have multiplicity of 1 or 2?

• 1

• 2

• 0

Does (1,0) have multiplicity of 1 or 2?

• 1

• 2

• 0

• (-2.55, 0), (2.55, 0)
• (-3, 0), (-2, 0), (2, 0), (3, 0)
• (0, 36)
• (0, -3), (0, -2), (0, 2), (0, 3)

• (1, 4)
• (0, 2)
• (-1, 0)
• (2, 0)

• (0, 4)
• (2, 0)
• (0, 2)
• (-1, 0)

• y = x(x - 3)(x - 2)
• y = x(x - 3)² (x+2)
• y = x(x + 3)² (x - 2)
• y = -x(x + 3)² (x - 2)

The function shown contains:

• Only one local maximum.

• Two local maximums.

• Two local minimums.

• Three local maximums