#4-3 Comparing Two Functions Represented in Different Ways

Front

What is a function?

Back

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.

Tags

CCSS.8.F.A.1

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What does it mean for a function to be linear?

Back

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is a y-intercept?

Back

The y-intercept is the point where a function crosses the y-axis, represented as (0, y).

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What is an increasing function?

Back

An increasing function is a function where, as the input values increase, the output values also increase.

Front

What is an exponential function?

Back

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

Front

How can you compare two functions?

Back

You can compare two functions by analyzing their graphs, equations, or tables to see differences in their rates of change, intercepts, and overall behavior.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What does it mean for functions to have a multiplying pattern?

Back

A multiplying pattern in functions indicates that the output is obtained by multiplying the input by a constant factor.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Tags

CCSS.8.EE.B.5

Front

How do you determine which function grows faster?

Back

To determine which function grows faster, compare their rates of change or slopes; the function with the greater slope increases more rapidly.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What is a constant function?

Back

A constant function is a function that does not change; it has the same output for every input and can be expressed as f(x) = c, where c is a constant.