The function below is continuous at which of the following values?f(x)=2x−3 3x−1−2×2+2xif x≤−3 if −3
To determine the values at which the function f(x) is continuous, we need to check if the function is continuous within each interval specified by the given conditions
To determine the values at which the function f(x) is continuous, we need to check if the function is continuous within each interval specified by the given conditions.
1. For the interval x ≤ -3:
The function f(x) is defined as f(x) = 2x – 3 for x ≤ -3. This expression represents a linear function, which is continuous for all real values of x. Therefore, f(x) is continuous for x ≤ -3.
2. For the interval -3 < x ≤ -1:
The function f(x) is defined as f(x) = 3x - 1 - 2x^2 + 2x for -3 < x ≤ -1. This expression represents a polynomial function. Polynomials are continuous for all real values of x, so f(x) is continuous for -3 < x ≤ -1.
3. For the interval -1 < x:
The function f(x) is not explicitly defined for this interval. It is not clear what f(x) is when x is greater than -1. Therefore, we cannot determine if f(x) is continuous for -1 < x.
In conclusion, the function f(x) = 2x - 3 for x ≤ -3 and f(x) = 3x - 1 - 2x^2 + 2x for -3 < x ≤ -1 is continuous for x ≤ -3 and -3 < x ≤ -1, respectively.
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To determine the values at which the function f(x) is continuous, we need to check if the function is continuous within each interval specified by the given conditions
To determine the values at which the function f(x) is continuous, we need to check if the function is continuous within each interval specified by the given conditions.
1. For the interval x ≤ -3:
The function f(x) is defined as f(x) = 2x – 3 for x ≤ -3. This expression represents a linear function, which is continuous for all real values of x. Therefore, f(x) is continuous for x ≤ -3.
2. For the interval -3 < x ≤ -1: The function f(x) is defined as f(x) = 3x - 1 - 2x^2 + 2x for -3 < x ≤ -1. This expression represents a polynomial function. Polynomials are continuous for all real values of x, so f(x) is continuous for -3 < x ≤ -1. 3. For the interval -1 < x: The function f(x) is not explicitly defined for this interval. It is not clear what f(x) is when x is greater than -1. Therefore, we cannot determine if f(x) is continuous for -1 < x. In conclusion, the function f(x) = 2x - 3 for x ≤ -3 and f(x) = 3x - 1 - 2x^2 + 2x for -3 < x ≤ -1 is continuous for x ≤ -3 and -3 < x ≤ -1, respectively.
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