SPRINGS When a weight up to 15 pounds is attached to a 4-inch spring, the length L, in inches, that the spring stretches is represented by the function Lw=12w+4, where w is the weight, in pounds, of the object. Select the domain and range of the function. Then determine whether it is one-to-one and whether it is discrete, continuous, or neither discrete nor continuous.

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MrRoyal MrRoyal · Answer 1 · 2022-08-27T11:39:50+02:00

The domain of the function is 0 <= w <= 11/12 and the range of the function is 4 <= L(w) <= 15

The function is given as:

L(w) = 12w + 4

The smallest value of w is 0, and the smallest value of L(w) is 4 i.e. when w = 0

The maximum value of L(w) is 15.

So, we have

12w + 4 = 15

Subtract 4 from the sides

12w = 11

Divide both sides by 12

w = 11/12

Hence, the domain of the function is 0 <= w <= 11/12 and the range of the function is 4 <= L(w) <= 15

The function is a linear function.

All linear functions are one-to-one functions

Hence, the function is a one-to-one function

Also, the function takes fractional values.

This is because the input of the function is weight

Weights are continuous values

Hence, the function is continuous

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