Question

What is the range of the function f(x)=6x-2 over the interval of 3

Answer 1

To find the range of the function f(x) = 6x - 2 over the interval of 3, we need to determine the set of all possible output values (y-values) that the function can take on within that interval.

The given function, f(x) = 6x - 2, is a linear function with a slope of 6 and a y-intercept of -2.

To find the range, we can consider the extremes of the interval. Let's substitute the values of 3 and -3 into the function:

For x = 3: f(3) = 6(3) - 2 = 18 - 2 = 16

For x = -3: f(-3) = 6(-3) - 2 = -18 - 2 = -20

Therefore, within the interval of 3, the range of the function f(x) = 6x - 2 is (-20, 16]. The range is represented as an interval because the function is continuous, and the range includes all values between -20 and 16, including the endpoints.

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