Question

Identify the set of x-values for which f(x )greater-than--or-equal-to 0.

Answers

Answer
Identify the set of x-values for which the graph of the piecewise-defined function is constant.
{x|x>-4}
{x|-1<x<2}
{x|-1<=x<=5}
(x|x<-4}
Answer
Identify the x-values for which f(x)>-2
A. {x|2<=x<=8}
B. {x|-2<=x<=2}
C. {x|-2<x<8}
D. {x|2<x<8}
Answered by GPT 3.5
To identify the set of x-values for which f(x) ≥ 0, we need to determine the values of x that make the function greater than or equal to zero.

Without knowing the specific function f(x), it is impossible to determine the exact set of x-values. The set of x-values for which f(x) ≥ 0 could be any range of values depending on the nature of the function.

For example, if the function f(x) is a linear equation, then the set of x-values for which f(x) ≥ 0 would be all x-values that produce a positive or zero y-value on the graph. This would be represented by the region above or on the x-axis.

However, if the function f(x) is a quadratic equation, then the set of x-values for which f(x) ≥ 0 could be two separate ranges of values, depending on where the graph intersects or touches the x-axis.

In summary, unless the specific function f(x) is provided, we cannot determine the exact set of x-values for which f(x) ≥ 0.
Answered by GPT 3.5
The set of x-values for which the graph of the piecewise-defined function is constant can be determined by looking at each piecewise-defined function individually.

1. {x|x > -4}: This means that the function is defined for all x-values greater than -4. Since the function is not restricted within a specific range, the graph of this piecewise-defined function will not be constant for any set of x-values.

2. {x|-1 < x < 2}: This means that the function is defined for all x-values between -1 and 2 (excluding -1 and 2). The graph of this piecewise-defined function is a line with a slope of 0, meaning it is constant for all x-values between -1 and 2 (excluding -1 and 2).

3. {x|-1 ≤ x ≤ 5}: This means that the function is defined for all x-values between -1 and 5 (including -1 and 5). The graph of this piecewise-defined function is constant for all x-values between -1 and 5 (including -1 and 5).

4. {x|x < -4}: This means that the function is defined for all x-values less than -4. Since the function is not restricted within a specific range, the graph of this piecewise-defined function will not be constant for any set of x-values.

In summary, the set of x-values for which the graph of the piecewise-defined function is constant is within the range -1 ≤ x ≤ 5.
Answered by GPT 3.5
To identify the x-values for which f(x) > -2, we need to find the range of values of x that produce a value of f(x) greater than -2.

Looking at the given options:

A. {x|2 <= x <= 8}: This set of x-values includes all values between 2 and 8, including the endpoints. However, it does not guarantee that f(x) will be greater than -2 for all values in this range.

B. {x|-2 <= x <= 2}: This set of x-values includes all values between -2 and 2, including the endpoints. However, it does not guarantee that f(x) will be greater than -2 for all values in this range.

C. {x|-2 < x < 8}: This set of x-values includes all values between -2 and 8, excluding the endpoints. This means that f(x) can be greater than -2 for all values within this range.

D. {x|2 < x < 8}: This set of x-values includes all values between 2 and 8, excluding the endpoints. This means that f(x) can be greater than -2 for all values within this range.

Out of the given options, both C and D are correct sets of x-values for which f(x) > -2.

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