12.3-12.4 Exponential functions

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a).

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What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than 0, or y > 0.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base 'b' is greater than 1, it is exponential growth. If the base 'b' is between 0 and 1, it is exponential decay.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line y = 0.

Front

What is the effect of changing the value of 'a' in an exponential function?

Back

Changing the value of 'a' affects the vertical stretch or compression of the graph. If 'a' is positive, the graph is above the x-axis; if negative, it is below.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, or (-∞, ∞).