Exponential Functions Key features

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is a constant (initial value) and 'b' is the base (growth or decay factor).

Front

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

Back

The base 'b' indicates the growth (b > 1) or decay (0 < b < 1) rate of the function.

Front

What is the range of an exponential function of the form f(x) = a * b^x where a > 0?

Back

The range is y > 0.

Front

What is the horizontal asymptote of an exponential function?

Back

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

Front

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

Back

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

Front

What is the y-intercept of the function f(x) = 3 * 2^x?

Back

The y-intercept is 3.

Front

What does it mean for an exponential function to have a y-intercept at a certain value?

Back

It means that when x = 0, the function's output (f(0)) equals that value.

Front

What is the initial value of the function f(x) = 3 * (0.5)^x?

Back

The initial value is 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 of the function.

Front

What is the significance of the coefficient 'a' in an exponential function?

Back

The coefficient 'a' represents the initial value or starting point of the function.