Exponential Functions

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.

Front

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

Back

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

Front

What is the general form of an exponential growth function?

Back

The general form is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(b^x) where 0 < b < 1.

Front

What does the 'a' represent in the exponential function y = a(b^x)?

Back

The 'a' represents the y-intercept of the function, which is the value of y when x = 0.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.

Front

What transformation does the equation y = 4^(x+1) + 3 represent?

Back

The transformation is a left shift by 1 unit and an upward shift by 3 units.

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a reciprocal; for example, b^(-x) = 1/(b^x).

Front

How can you identify exponential growth from a table of values?

Back

In exponential growth, the ratio of consecutive y-values increases as x increases.

Front

How can you identify exponential decay from a table of values?

Back

In exponential decay, the ratio of consecutive y-values decreases as x increases.