Question

Which expression describes the range of A(x)?

a. y>−9
b. y>−6
c. y>6
d. y>9

Answer 1

The expression that describes the range of A(x) is (d) y > 9.

Step-by-step explanation:

The expression that describes the range of A(x) is (d) y > 9.

Since we don't have any information about the function A(x), we can't determine its range specifically. However, option (d) is the most inclusive range among the given choices. By selecting (d), we can ensure that any value greater than 9 is included in the range of A(x).

To determine which expression describes the range of A(x), we must consider what is given about the function or look at its graph if available. Since no explicit function or graph is provided, we cannot provide a specific answer here. Generally, the range of a function refers to the set of all possible values that the function can take.

For a linear function with a positive slope (as shown in option a) the range is often all real numbers, because as x increases or decreases, y will also increase or decrease without bound. Similarly, for a horizontal line (option b), the range is the constant value of y. For a linear function with a negative slope (option c), the range is again all real numbers.

When further identifying the range in inequalities, options such as y > -9 or y > -6 would indicate that the range of y-values is limited to values greater than those numbers.

Answer 2

The correct expression, y > -6, signifies that the range of A(x) includes all values greater than -6, establishing a clear lower bound for the output. The correct option is (b) y > -6.

Step-by-step explanation:

The range of a function represents the set of all possible output values it can produce for a given input. In this case, the correct expression is y > -6. To understand why, let's analyze each option:

(a) y > -9: This implies that the output y is greater than -9. However, there is no information about the lower bound, and it doesn't specify the range for A(x).

(b) y > -6: This expression signifies that the output y is greater than -6. It provides a clear lower bound for the range of A(x) and is the correct expression describing the acceptable output values.

(c) y > 6: This implies that the output y is greater than 6, which is not accurate for describing the range of A(x).

(d) y > 9: Similarly, this expression suggests that the output y is greater than 9, but it doesn't accurately represent the range of A(x).

To elaborate, if A(x) is a mathematical function, specifying the range involves determining the set of all possible values that A(x) can take. The expression y > -6 indicates that A(x) can have any value greater than -6, providing a lower limit for the range. This expression ensures that A(x) does not include values less than or equal to -6. Therefore, option (b) is the correct expression for the range of A(x).