Equations b) x - 12 = 34 and c) 2y = -12 represent functions because they satisfy the definition of a function where every input has a single, unique output.
The question asks which equation represents a function. To determine if an equation represents a function, each input value should correspond to exactly one output value. Let's analyze the given equations:
- a) x = 13 is a vertical line and thus does not represent a function, since it violates the definition of a function. Each input has infinitely many outputs.
- b) x - 12 = 34 is a simple algebraic equation that can be solved for x, giving a single value. This represents a function, as each input has only one output.
- c) 2y = -12 is an equation that can be solved for y, giving a single value as an output for the 'function', which in this case is a constant function.
- d) 2x - 4x = 7 is an algebraic equation that can also be solved for x. However, once solved, it does not represent a variable input and output relationship typical of a function.
- e) x/2 = 15 is another algebraic equation solvable for x. Like choice 'b', it also represents a function.
From the options provided, b) x - 12 = 34 and c) 2y = -12 represent functions using the definition of a function in mathematics.