Comparing Linear, Exponential, and Quadratic Functions

The video tutorial covers the three main types of functions: linear, exponential, and quadratic. It explains how to identify these functions by graphing and using differences. The tutorial also demonstrates how to write rules for these functions and introduces the concept of average rate of change, which is foundational for calculus. Examples are provided to illustrate each concept, and students are encouraged to take notes and practice identifying and writing function rules.

What is the standard form of a linear function?

• y = mx + b

• y = ab^x

• y = ax^2 + bx + c

• y = a + bx

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Which component represents the slope in a linear function?

• a

• b

• m

• c

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How can you visually identify a quadratic function from a set of points?

• The points are randomly distributed.

• The points form a straight line.

• The points form a parabola.

• The points increase exponentially.

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What indicates a function is exponential when analyzing changes in y values?

• Constant addition

• No constant change

• Constant subtraction

• Constant multiplication

What does a 'second difference' being constant signify about a function?

• It is linear

• It is quadratic

• It is undefined

• It is exponential

In a quadratic function, what does the term 'vertex' refer to?

• The highest or lowest point on the graph

• The point where the graph crosses the y-axis

• The difference between consecutive y-values

• The constant rate of change

What is the significance of the roots or zeros in a quadratic equation?

• They indicate where the function crosses the x-axis.

• They determine the slope of the function.

• They show the maximum value of the function.

• They represent the y-intercept of the function.

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What is the average rate of change used to determine in non-linear functions?

• The slope between any two given points

• The vertex of the function

• The quadratic peak points

• The exponential growth factor

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How is the average rate of change calculated between two points?

• Add the y-values and multiply by the x-values

• Divide the y-values by the x-values

• Multiply the y-values and subtract the x-values

• Subtract the y-values and divide by the x-values

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CCSS.8.F.B.4

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What foundational concept of calculus is introduced through the average rate of change?

• Limits

• Differentiation

• Algebraic manipulation

• Integration

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