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Select all the correct answers.Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x

Question

Select all the correct answers.Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x

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Solution

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An equation can represent a function if for any x in the equation, there is exactly one corresponding y.

Let's check each equation:

  1. 2x + 3y = 10: This equation can be rewritten as y = (10 - 2x) / 3. For each x, there is exactly one y. So, this equation represents a function.

  2. 4x = 16: This equation can be rewritten as x = 4. This is a vertical line in the coordinate plane and does not pass the vertical line test. So, this equation does not represent a function.

  3. 2x − 3 = 14: This equation can be rewritten as x = (14 + 3) / 2. For each x, there is exactly one y. So, this equation represents a function.

  4. 3y = 18: This equation can be rewritten as y = 6. This is a horizontal line in the coordinate plane and passes the vertical line test. So, this equation represents a function.

  5. 14.6 = 2x: This equation can be rewritten as x = 14.6 / 2. For each x, there is exactly one y. So, this equation represents a function.

So, the equations that represent functions are: 2x + 3y = 10, 2x − 3 = 14, 3y = 18, and 14.6 = 2x.

This problem has been solved

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