Exam Review - Transformations and Sequences

Front

What is a transformation in mathematics?

Back

A transformation is an operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Front

Define translation in the context of graph transformations.

Back

Translation is a type of transformation that shifts a graph horizontally, vertically, or both without changing its shape.

Front

What does it mean to compress a graph vertically?

Back

Vertical compression occurs when the graph of a function is squeezed towards the x-axis, making it shorter.

Front

What is the effect of shifting a graph 4 units to the left?

Back

Shifting a graph 4 units to the left means that every point on the graph moves 4 units in the negative x-direction.

Front

How do you determine the explicit formula for a sequence?

Back

To determine the explicit formula for a sequence, identify the pattern in the sequence and express it in the form a_n = f(n), where f(n) is a function of n.

Front

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

Back

The formula for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What does the notation a_n = 4n + 11 represent?

Back

This notation represents a sequence where each term is calculated by multiplying the term's position n by 4 and then adding 11.

Front

What transformation is applied to the function f(x) = x^2 to get g(x) = (x + 4)^2?

Back

The transformation is a shift of 4 units to the left.

Front

How do you find the common difference in a sequence?

Back

The common difference in a sequence is found by subtracting any term from the subsequent term.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.