Linear and Exponential Functions Review

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It grows or decays at a constant percentage rate.

Front

How can you identify a linear relationship from a table of values?

Back

In a linear relationship, the difference between consecutive y-values is constant for equal intervals of x.

Front

How can you identify an exponential relationship from a table of values?

Back

In an exponential relationship, the ratio of consecutive y-values is constant for equal intervals of x.

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What is the slope of a linear function?

Back

The slope of a linear function (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

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What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It represents the point where the line crosses the y-axis.

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What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage, leading to faster growth over time.

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What does it mean if a relationship is neither linear nor exponential?

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If a relationship is neither linear nor exponential, it does not follow a straight line or an exponential curve, and may involve more complex patterns or functions.

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What is an example of a real-world situation that can be modeled by a linear function?

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An example is calculating the total cost of items purchased at a constant price, such as y = 5x, where y is total cost and x is the number of items.