Linear vs Exponential

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What is a linear function?

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A linear function is a function that creates a straight line when graphed. It has a constant rate of change 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 an exponential function?

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An exponential function is a function in which an independent variable is in the exponent. It can be expressed in the form y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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How do you identify a linear function from a graph?

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A linear function can be identified by a straight line on the graph. The slope is constant, and the y-values change at a constant rate as the x-values change.

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How do you identify an exponential function from a graph?

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An exponential function can be identified by a curve that increases or decreases rapidly. The rate of change is not constant; it grows or shrinks exponentially.

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What is the difference between linear and exponential growth?

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

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What does it mean for a function to be neither linear nor exponential?

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A function that is neither linear nor exponential does not fit the characteristics of either type. Its graph may be curved in a way that does not represent constant or exponential change.

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates how steep the line is.

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What is the y-intercept of a linear function?

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The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

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What is a common example of a linear function in real life?

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A common example of a linear function is calculating the total cost of items when each item has a fixed price.

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What is a common example of an exponential function in real life?

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A common example of an exponential function is population growth, where the population increases by a percentage over time.