6.2 Exponential Key Charateristics

Front

What is the x-intercept of an exponential function?

Back

The x-intercept is the point where the graph crosses the x-axis, which occurs when y=0. For most exponential functions, there is no x-intercept.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph approaches but never touches or crosses. For the function f(x) = a^x, the vertical asymptote is typically at x=0.

Front

How do you determine the equation for exponential growth?

Back

The general form is y = a(b)^x, where 'a' is the initial amount, 'b' is the growth factor, and 'x' is time.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote is a horizontal line that the graph approaches as x approaches infinity. For the function f(x) = a^x, the horizontal asymptote is usually y=0.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, represented as (0, ∞).

Front

How do you calculate the population after a certain time with exponential growth?

Back

Use the formula y = a(2)^(t/d), where 'a' is the initial population, 't' is the total time, and 'd' is the doubling time.

Front

What does it mean for a function to be increasing exponentially?

Back

An exponentially increasing function grows at a rate proportional to its current value, leading to rapid growth as time progresses.

Front

What is the significance of the base in an exponential function?

Back

The base determines the growth rate; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

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

Back

The y-intercept is found by evaluating the function at x=0, which gives y = a(b)^0 = a.