How to dynamically add textbox in form?

Hello,

Which would be the best element to add to be able to ask a question and have the user add multiple text responses. 

Yes it is possible to achieve your requirement by taking advantage of following widgets and see if that fits into your requirement:

Configurable List

Infinite List

The following guide should help you how to add widget in form:  https://www.jotform.com/help/252-How-to-Add-a-Widget-to-Your-Form 

That’s great, I am using the configurable list and love it. I’m just wondering if there is a way to turn off the ability for the user to add a line. Some forms I will require the ability to have the user add rows but other I don’t them to be able to.
Thank you,
Samantha Shepperd | Toronto Branch Administrator
Fujitec Canada Inc.
15 East Wilmot St.
Richmond Hill, ON L4B 1A3
P 905 731 8681 x 214
F 905 731 8425
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In the configurable list widget settings, there are options to set the minimum and maximum number of rows:

If this is set to "1", users will not be able to add more rows.