#4 | Flashcardizz (6.2)

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛(x), which gives the number that, when multiplied by itself three times, equals x.

Front

How do you shift a function to the right and up?

Back

To shift a function to the right by 'h' units, replace x with (x - h). To shift it up by 'k' units, add k to the function. For example, f(x) = ∛(x) shifted right 3 and up 2 is f(x) = ∛(x - 3) + 2.

Front

What are extrema in a graph?

Back

Extrema are the maximum and minimum values of a function. The absolute maximum is the highest point, while the absolute minimum is the lowest point on the graph.

Front

How do you find the range of a function?

Back

The range of a function is the set of all possible output values (y-values). To find it, analyze the function's behavior and identify the lowest and highest values it can take.

Front

What is the square root function?

Back

The square root function is defined as f(x) = √x, which gives the non-negative value whose square is x. It is only defined for x ≥ 0.

Front

What does the domain of a function represent?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant 'k' to a function f(x) shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the significance of the absolute maximum and minimum?

Back

The absolute maximum is the highest point on the graph, while the absolute minimum is the lowest point. They are important for understanding the overall behavior of the function.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase. It is decreasing if the output values fall as the input values increase.

Front

What is a vertical shift in a function?

Back

A vertical shift occurs when a constant is added or subtracted from a function. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down.