Exponential F(x), Rate of Change, Increase/Decrease, Sequences

Front

What is an explicit equation for an arithmetic sequence?

Back

An explicit equation for an arithmetic sequence is of the form f(n) = a + d(n - 1), where 'a' is the first term and 'd' is the common difference.

Front

Given the first term is 3 and the common difference is 5, what is the explicit equation for the sequence?

Back

f(n) = 3 + 5(n - 1)

Front

What does it mean for a function to be positive?

Back

A function is positive when its output values are greater than zero for the given input values.

Front

Identify the interval where the function is positive: f(x) = x^2 - 9.

Back

The function is positive in the interval (-3, 3).

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

Given the first term is 10 and the common difference is 3, what is the explicit equation for the sequence?

Back

f(n) = 10 + 3(n - 1)

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

How do you determine if a function is increasing or decreasing on an interval?

Back

You can determine this by analyzing the derivative of the function or by evaluating the function's values at endpoints of the interval.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The formula is f(n) = a + d(n - 1), where 'a' is the first term and 'd' is the common difference.