Accommodated Lesson 3.6, 3.7 and 4.3 Flashcard

Front

What is a vertical translation in function transformations?

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.

Front

What happens to the graph of f(x) when it is replaced with f(x + k)?

Back

The graph of f(x) shifts horizontally. If k is positive, the graph shifts left by k units; if k is negative, it shifts right by |k| units.

Front

Define the term 'parent function' in mathematics.

Back

A parent function is the simplest form of a function type, from which other functions in the same family are derived. For example, the parent function of linear functions is f(x) = x.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by. It is calculated by subtracting any term from the subsequent term.

Tags

CCSS.HSF.BF.A.2

Front

If f(x) = |x|, what is the effect of replacing it with f(x) = |x| + 2?

Back

The graph of f(x) = |x| + 2 is a vertical translation of the parent function f(x) = |x|, shifted up by 2 units.

Front

How does the function g(x) = f(x - 3) transform the graph of f(x)?

Back

The function g(x) = f(x - 3) represents a horizontal translation of the graph of f(x) to the right by 3 units.

Front

What is the effect of a negative value in front of a function, such as -f(x)?

Back

A negative value in front of a function reflects the graph across the x-axis. For example, if f(x) is a positive function, -f(x) will be negative for all x.

Front

What does the notation f(x) = |x - 2| represent?

Back

This notation represents a function that is a transformation of the parent absolute value function, shifted horizontally to the right by 2 units.

Front

If a function is defined as f(x) = |x + 2|, what is the transformation from the parent function?

Back

The function f(x) = |x + 2| is a horizontal translation of the parent function f(x) = |x|, shifted left by 2 units.

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.

Tags

CCSS.HSF-IF.C.7D