Lesson 3.6, 3.7 and 4.3 Flashcard

Front

What is a vertical translation in a function?

Back

A vertical translation occurs when a function is shifted up or down on the graph. For example, if f(x) is replaced with f(x) + k, the graph shifts vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What is the general form of an absolute value function?

Back

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is found by subtracting any term from the subsequent term. For example, in the sequence 25, 34, 43, the common difference is 34 - 25 = 9.

Front

What are the next three terms in the arithmetic sequence: 25, 34, 43, 52?

Back

The next three terms are 61, 70, 79.

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

Front

What is the significance of the vertex in an absolute value function?

Back

The vertex of an absolute value function is the point where the graph changes direction. It represents the minimum or maximum value of the function.

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant. If the difference varies, it is not arithmetic.

Front

What is the common difference in the sequence: -33, -24, -15, -6?

Back

The common difference is 9, calculated as -24 - (-33) = 9.

Front

What is the formula to find the 26th term in the arithmetic sequence: -15, -35, -55, -75?

Back

Front

What does it mean to reflect a function across the x-axis?

Back

Reflecting a function across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph. This is achieved by replacing f(x) with -f(x).