Question
Determine whether the equation represents a function.
y equals x squared plus 6
Question content area bottom
Part 1
Does the equation represent a function?
y equals x squared plus 6
Question content area bottom
Part 1
Does the equation represent a function?
Answers
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Answered by
GPT-4o mini
To determine whether the equation \( y = x^2 + 6 \) represents a function, we can analyze the definition of a function. A relation is a function if every input (or \( x \)-value) has exactly one output (or \( y \)-value).
In this case, the equation \( y = x^2 + 6 \) allows you to input any real number for \( x \), and you will always get one corresponding \( y \)-value. Specifically, for each \( x \):
- If you plug in \( x = 1 \), then \( y = 1^2 + 6 = 7 \).
- If you plug in \( x = -1 \), then \( y = (-1)^2 + 6 = 7 \) (same \( y \)-value, but different \( x \)-values).
- If you plug in \( x = 0 \), then \( y = 0^2 + 6 = 6 \).
Since for every possible \( x \) there is exactly one corresponding \( y \), the equation does represent a function.
Thus, the answer is **Yes, it represents a function.**
In this case, the equation \( y = x^2 + 6 \) allows you to input any real number for \( x \), and you will always get one corresponding \( y \)-value. Specifically, for each \( x \):
- If you plug in \( x = 1 \), then \( y = 1^2 + 6 = 7 \).
- If you plug in \( x = -1 \), then \( y = (-1)^2 + 6 = 7 \) (same \( y \)-value, but different \( x \)-values).
- If you plug in \( x = 0 \), then \( y = 0^2 + 6 = 6 \).
Since for every possible \( x \) there is exactly one corresponding \( y \), the equation does represent a function.
Thus, the answer is **Yes, it represents a function.**
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