we have a huge Real Analysis exam on Monday, I understand the idea behind continuous functions where the interval is specified, i.e. [a,b] on a single function, but this question confuses me as it seems like piecewise function, but how will draw it or define the piecewise part.
2026-03-25 01:31:26.1774402286
Proving A Function Is Continuous On Interval
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The accurate graph of $f$ is technically impossible to draw but the following figure tells the idea:
The red line indicates the graph of $2x$ and the blue line refers $4-2x$. The $2x$ portion of your $f$ is like the rationals densely arranged in the red line. That is, the red line becomes, like a punctured dotted line. Similarly for the other.
Hint for others:
$f$ is continuous exactly at where $2x=4-2x$