Exponential Graphs Review

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

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in f(x) = a * b^x is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when 'b' is between 0 and 1, resulting in a decrease in value as 'x' increases.

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 where the graph intersects the y-axis, which occurs at (0, a).

Front

How do you identify an exponential function from an equation?

Back

An exponential function can be identified by the variable 'x' being in the exponent, such as in y = a * b^x.

Front

What is the general form of an exponential decay function?

Back

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

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than 0 if it is an exponential growth function, or all real numbers less than a certain value if it is an exponential decay function.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is the line y = 0, which the graph approaches but never touches.

Front

How can you determine if a function is exponential from a table of values?

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 1) results in slower growth.