Module 6 Test Remediation

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all possible input values (x) for which the function is defined. For square root functions, this typically means the expression inside the radical must be greater than or equal to zero.

Front

How do you determine the domain of the function f(x) = √(x-4) - 2?

Back

To find the domain, set the expression inside the square root greater than or equal to zero: x - 4 ≥ 0. This gives x ≥ 4, so the domain is [4, ∞).

Front

What is the simplified form of the expression 16 + 16?

Back

The simplified form is 32.

Front

What is the domain of the function f(x) = √(x + 1)?

Back

The domain is x ≥ -1, since the expression inside the square root must be non-negative.

Front

What is the cube root of 8?

Back

The cube root of 8 is 2, since 2 × 2 × 2 = 8.

Front

What does it mean for a function to be defined?

Back

A function is defined for a particular input if there is a corresponding output. For example, a square root function is defined only for non-negative inputs.

Front

How do you find the range of a radical function?

Back

The range of a radical function can be found by determining the possible output values (y) based on the domain. For example, the range of f(x) = √(x-4) - 2 is y ≥ -2.

Front

What is the significance of the vertex in a radical function graph?

Back

The vertex represents the minimum point of the graph for functions that open upwards, or the maximum point for functions that open downwards.

Front

What is the general form of a square root function?

Back

The general form is f(x) = a√(x - h) + k, where (h, k) is the vertex of the graph.

Front

How do you identify the transformations of a radical function?

Back

Transformations can be identified by examining changes in the function's equation, such as shifts (h, k), reflections (negative a), and stretches/compressions (absolute value of a).