#4-3 Comparing Two Functions Represented in Different Ways

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What is a function?

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A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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What does it mean for a function to be linear?

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A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a y-intercept?

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The y-intercept is the point where a function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

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How can you compare two functions represented in different ways?

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You can compare their outputs for the same inputs, analyze their graphs, or evaluate their equations to determine similarities and differences.

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What does it mean for a function to be increasing?

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A function is increasing if, as the input values increase, the output values also increase.

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What is the difference between a linear function and an exponential function?

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A linear function increases by a constant amount, while an exponential function increases by a percentage rate, leading to faster growth over time.

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How do you find the starting value of a function?

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The starting value of a function is typically found by evaluating the function at x = 0, which gives the y-intercept.

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What is the significance of comparing starting values in real-world scenarios?

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Comparing starting values helps determine which option is more favorable or advantageous, such as in salary comparisons or initial measurements.

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What is a comparative question?

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A comparative question asks you to evaluate two or more items to determine which one has a certain quality or characteristic.