Exponentials Unit Flashcard

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function intersects the y-axis, represented as (0, y).

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 the base (a positive real number), and x is the exponent.

Front

What is the difference between arithmetic and geometric sequences?

Back

An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.

Front

Identify the initial value in the function f(x)=13(0.27)^x.

Back

The initial value (y-intercept) is 13, which is the value of the function when x=0.

Front

How do you calculate the average rate of change of a function?

Back

The average rate of change from x=a to x=b is calculated as (f(b) - f(a)) / (b - a).

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula a_n = a * r^(n-1), where a is the first term and r is the common ratio.

Front

What does it mean for a sequence to be neither arithmetic nor geometric?

Back

A sequence is neither arithmetic nor geometric if it does not have a constant difference or a constant ratio between its terms.

Front

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

Back

The base of an exponential function determines the rate of growth or decay; if the base is greater than 1, the function grows, and if it is between 0 and 1, it decays.

Front

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

Back

To find the y-intercept of an exponential function f(x) = a * b^x, evaluate f(0), which gives the point (0, a).

Front

What is the 7th term of the geometric sequence defined by a_n = -3(2)^(n-1)?

Back

The 7th term is -192, calculated as a_7 = -3(2)^(7-1) = -3(16) = -192.