Question

If the rule of a relation is "y is found by squaring x and then adding 3," is the relation a function? Responses A No; because y = 19 if x = 4 or x = −4.No; because y = 19 if x = 4 or x = −4. B Yes; because each y can come from only one x.Yes; because each y can come from only one x. C Yes; because each x will result in exactly one y.Yes; because each x will result in exactly one y. D No; because both x = −8 and x = 8 result in y = 67.

Answer 1

The rule 'y is found by squaring x and then adding 3' represents a function, as each unique x-value corresponds to a single y-value, satisfying the definition of a function where each input has exactly one output. Therefore correct option is A

Step-by-step explanation:

If the rule of a relation is y is found by squaring x and then adding 3, the relation can be expressed as the equation

y = x^2 + 3.

To determine if this relation is a function, we need to consider if each x-value corresponds to exactly one y-value.

When looking at this equation, for any given x-value, there will only be one possible y-value because squaring a number (whether it's negative or positive) always results in a positive value, and adding 3 to it gives us a single, unique result.

Therefore, regardless of whether x is 4 or -4, each instance of x gives us a single y-value.

So, the relation described by y = x^2 + 3 is indeed a function, as each x will result in exactly one y-value.