Suppose that this is the function for the area of a frame: f(x)=4x2+72x+320 If the frame must be at at least 1 inch and no more than 3 inches wide. What re the domain and the range of the function?

Question

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Answer 1

The domain of a function means the x values that the function is “allowed” to cover. The range is referring to the y values that the function is “allowed” to cover.

For this problem, you have a function (f(x)=4x²+72x+320) that represents frame size, and a boundary for how many inches the width can be (between 1 and 3 inches). This boundary for the width is going to be the domain for the function.

For the range, the values aren’t given to you, but we can find them! If the x values need to fall between two points, that means the y values need to fall between those two points as well (1 and 3).

Solve for f(1): 4(1)²+72(1)+320 = 396

Solve for f(3): 4(3)²+72(3)+320 = 572

The y values need to fall between 396 and 572, so that is the range.

Answer: D = [1,3] R = [396,572]