Found an older thread about this, but the proposed tricks are for labeling text labels, not axes.
Honestly, I'm not sure how to accomplish this for axes, short of the (very hackish) approach of doing multiple sheets, identical except that they each support only one currency, and then layer them on a dashboard using the trick to always collapse all but 1 of the sheets in response to a parameter. http://onlinehelp.tableau.com/current/pro/desktop/en-us/help.htm#dashboards_sheet_selector.html
Personally, I try to avoid that trick because potential increased complexity of maintenance. I would favor the recommendation of Russell Christopher in that first thread I linked: don't show any currency symbol and (if needed) supplement the chart with a caption or other informational block that calls out what currency the numbers represent.
You can 'trick' the user that you are showing a different currency by just creating 2 visualizations.
Viz 1 = Show the line chart you have with the USD currency
Viz 2 = Show the line chart you have with the EUR currency
Put them both on a dashboard and use the following trick: Use Parameters to Add Multiple Views to Your Viz | Tableau Software
This makes it possible to work with a parameter to switch between your two visualizations.
Hope this helps you!
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You cannot dynamically change the currency prefix on the axis.
If it were me, I would remove the currency format all together and just show the numbers. Then I would remove the axis title and create a new calculated field like;
IF [parameterCurrency] = "USD" then "Sales in $ (USD)" elseif [paramaterCurrency] = "EUR" then "Sales in € (EUR)" end
I'd add that new dimension to the rows shelf, rotate the header text and it would look something like this;
Then when you change your parameter, the rotated dimension header will update.
Tom, that's a great trick!
Thanks Tom! This is exactly what I needed.