Find the Zeros for the Polynomial Function and Give the Multiplicity

question 237

Multiple Choice

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
- $$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

• A) \(- 1\), multiplicity 1 , crosse the \(x\)-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• - 8 , multiplicity 1 , crosses the \(x\)-axis.
• B) 8 , multiplicity 1 , crosses the x-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• - 8 , multiplicity 1 , crosses the \(x\)-axis.
• C) 1 , multiplicity 2 , touches the \(x\)-axis and turns around;
• \(- 8\), multiplicity 1 , crosses the x-axis.
• D) \(- 1\), multiplicity 1 , touches the \(x\)-axis and turns around; 1 , multiplicity 1 , touches the \(x\)-axis and turns around;
• - 8 , multiplicity 1 , touches the \(x\)-axis and turns around Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.

Explain the procedure and implications of shaping and extinction in learning.

Understand the role of reinforcement schedules in maintaining behavior.

Apply knowledge of operant conditioning to real-world training and behavior modification.

Grasp the importance of discriminative stimuli in signaling reinforcement.

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Definitions:

Upward-Sloping

Characteristic of a line or curve that rises as it moves from left to right, used to describe certain types of supply curves.

Production Possibilities Curve

A graphical representation showing the maximum quantity of goods that can be produced using limited resources to the fullest extent, at a given technology level.

Maximum Combinations

Maximum combinations represent the highest number of product or service bundles that can be produced or offered given a set of resources and technology.

Linear Equation

A mathematical expression that represents a straight line when plotted on a graph, typically in the form y = mx + b.