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.

Tags

CCSS.HSF-IF.C.8B

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).

Tags

CCSS.HSF-IF.C.7E

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'.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-LE.A.1A

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.

Tags

CCSS.HSF-IF.C.7E