Algebraic Reasoning Unit 5 Review

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the line y = 0.

Front

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

Back

The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which gives the point (0, a).

Front

What is the general form of an exponential decay function?

Back

The general form is f(t) = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What does the base of an exponential function indicate?

Back

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

Front

How do you determine the x-intercept of an exponential function?

Back

Exponential functions do not have x-intercepts because they never cross the x-axis; they approach it asymptotically.

Front

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

Back

The y-intercept is the value of the function when x = 0, which is f(0) = 3(2)^0 = 3, indicating the starting value of the function.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

How can you model a situation with a decreasing quantity using an exponential function?

Back

You can model it with f(t) = a(1 - r)^t, where a is the initial amount and r is the decay rate.

Front

What is the relationship between the graphs of f(x) = 2(5)^x and g(x) = 4x + 3?

Back

f(x) is an exponential function that grows rapidly, while g(x) is a linear function. They have different growth rates and shapes.

Front

What does it mean for a function to have a domain of all real numbers?

Back

It means that the function can accept any real number as input, and there are no restrictions on the values of x.