To find which option represents the graph of the function \( y = x + 2 \), we can substitute the x-values from each option into the equation and see if the corresponding y-values match.
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Option 1: (-2,0) (0,2)
- For \( x = -2 \): \( y = -2 + 2 = 0 \) (This point is correct)
- For \( x = 0 \): \( y = 0 + 2 = 2 \) (This point is correct)
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Option 2: (-4,2) (-2,0) (0,2)
- For \( x = -4 \): \( y = -4 + 2 = -2 \) (This point is incorrect)
- For \( x = -2 \): \( y = -2 + 2 = 0 \) (This point is correct)
- For \( x = 0 \): \( y = 0 + 2 = 2 \) (This point is correct)
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Option 3: (0,2) (2,0)
- For \( x = 0 \): \( y = 0 + 2 = 2 \) (This point is correct)
- For \( x = 2 \): \( y = 2 + 2 = 4 \) (This point is incorrect)
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Option 4: (-2,0) (0,2) (2,0)
- For \( x = -2 \): \( y = -2 + 2 = 0 \) (This point is correct)
- For \( x = 0 \): \( y = 0 + 2 = 2 \) (This point is correct)
- For \( x = 2 \): \( y = 2 + 2 = 4 \) (This point is incorrect)
Based on this analysis, the points in Option 1 \( (-2,0) \) and \( (0,2) \) both satisfy the equation \( y = x + 2 \).
Final answer: Option 1: (-2,0) (0,2).