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

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 value of f(0), which equals 'a'.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the function's base 'b' is greater than 1, resulting in values that increase rapidly as 'x' increases.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the function's base 'b' is between 0 and 1, leading to values that decrease rapidly as 'x' increases.

Front

How do you identify the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the function's output changes for each unit increase in 'x', represented by the base 'b'.

Front

What is the formula for finding the y-intercept of f(x) = a(b)^x?

Back

The y-intercept is found by evaluating f(0), which gives f(0) = a(b)^0 = a.

Front

If f(x) = 3(2)^x, what is the y-intercept?

Back

The y-intercept is 3, since f(0) = 3(2)^0 = 3.

Front

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

Back

Changing the base 'b' affects the rate of growth or decay; a larger base results in faster growth, while a smaller base (greater than 0) results in slower growth or decay.

Front

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

Back

If the ratio of consecutive outputs is constant, the function is exponential.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the x-axis but never touches it.