To determine at which points the functions \( f(x) \) and \( g(x) \) have the same y-value, we need to find pairs of \( x \) values such that \( f(a) = g(b) \) for given values of \( a \) and \( b \).
The options you provided seem to list relationships between the values of \( f \) and \( g \) at specific points:
- \( f(0) = g(0) \) and \( f(2) = g(2) \)
- \( f(2) = g(0) \) and \( f(0) = g(4) \)
- \( f(2) = g(0) \) and \( f(4) = g(2) \)
- \( f(2) = g(4) \) and \( f(1) = g(1) \)
To determine which pairs indicate the same y-values, you should inspect each statement individually.
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Option 1 states that both functions are equal at \( x = 0 \) and \( x = 2 \). This indicates they have the same y-values at those points directly.
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Option 2 suggests that \( f(2) \) equals \( g(0) \) and \( f(0) \) equals \( g(4) \). This does not ensure they are equal at the same x-value but rather suggests relationships between different values.
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Option 3 is similar to Option 2 but connects \( f(2) \) to \( g(0) \) and pairs \( f(4) \) with \( g(2) \), again not necessarily indicating they are equal at the same x.
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Option 4 again connects \( f(2) \) and \( g(4)\) but claims simultaneous equality at \( x=1\) for both \( f \) and \( g\).
To solve this properly, you would need to examine the graphs of \( f(x) \) and \( g(x) \) to see if any of these statements are true. If you have access to this graph, simply look for intersections or the y-values at the specified \( x \) points.
If you are deciding based purely on the summarized pairs without graphing, Option 1 appears to present the clearest cases of equality for direct points.
Therefore, the functions \( f(x) \) and \( g(x) \) have the same y-values at the points specified in Option 1: \( f(0) = g(0) \) and \( f(2) = g(2) \).