1. f(x) = (x-y)² + 1: This is a function because for every value of x, there is a unique value of f(x) determined by the expression (x-y)² + 1. The values of y do not affect the function's definition as long as the input x remains the same.
2. 2x = -4: This is an equation, not a function. It represents a relationship between x and -4, where there is a specific value of x (-2 in this case) that satisfies the equation. However, there are infinitely many values of x that can satisfy this equation, so it does not define a unique output for each input, which is a requirement for a function.
3. |x+1| = y: This equation represents a relationship between x and y, where the value of y is equal to the absolute value of (x+1). Similar to the previous example, there can be multiple values of x that satisfy this equation, so it does not define a unique output for each input and is therefore not a function.
Step-by-step explanation:
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Answer:
1. f(x) = (x-y)² + 1: This is a function because for every value of x, there is a unique value of f(x) determined by the expression (x-y)² + 1. The values of y do not affect the function's definition as long as the input x remains the same.
2. 2x = -4: This is an equation, not a function. It represents a relationship between x and -4, where there is a specific value of x (-2 in this case) that satisfies the equation. However, there are infinitely many values of x that can satisfy this equation, so it does not define a unique output for each input, which is a requirement for a function.
3. |x+1| = y: This equation represents a relationship between x and y, where the value of y is equal to the absolute value of (x+1). Similar to the previous example, there can be multiple values of x that satisfy this equation, so it does not define a unique output for each input and is therefore not a function.
Step-by-step explanation:
I hope it helps