AP PreCalc 2.1- 2.6 Review

Front

What is the y-intercept of the function y=4(2)^x?

Back

The y-intercept is the point where the graph intersects the y-axis, which occurs when x=0. For y=4(2)^x, the y-intercept is (0, 4).

Front

How do you write a formula for a geometric sequence?

Back

A geometric sequence can be expressed in the form a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio. For the sequence 4, 12, 36, 108, the formula is a_n = 4(3^(n-1)).

Front

What is the effect of subtracting a constant from an exponential function?

Back

Subtracting a constant from an exponential function, such as f(x) = 3^x - 4, shifts the graph down by that constant value. In this case, the graph of f(x) is shifted 4 units down from g(x) = 3^x.

Front

How can you determine the function that models a set of data points?

Back

To determine the function that models a set of data points, analyze the pattern of the data. For example, if the data follows an exponential growth pattern, you can use the form f(x) = a * b^x, where 'a' is a constant and 'b' is the growth factor.

Front

What transformation occurs when you shift an exponential function to the right?

Back

Shifting an exponential function to the right by 'h' units can be represented by replacing x with (x-h) in the function. For example, the transformation of y=2^x to the right by 3 units results in y=2^(x-3).

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 that represents the initial value, and 'b' is the base that determines the growth or decay rate.

Front

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

Back

To find the y-intercept of an exponential function, substitute x=0 into the function. The resulting value will give you the y-coordinate of the y-intercept.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is the factor by which each term is multiplied to get the next term. For the sequence 4, 12, 36, 108, the common ratio is 3.

Front

What does it mean for a function to be transformed vertically?

Back

A vertical transformation involves shifting the graph of a function up or down. For example, adding a constant to a function shifts it up, while subtracting a constant shifts it down.

Front

How do you identify the transformation of a function from its equation?

Back

To identify the transformation of a function from its equation, compare it to the parent function. Look for changes in the form of addition, subtraction, multiplication, or division that indicate shifts, stretches, or reflections.