jats:titleAbstract</jats:title>jats:pIn this paper, we study some properties of Takagi functions and their level sets. We show that for Takagi functions jats:inline-formulajats:alternativesjats:tex-math$$T_{a,b}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:msubmml:miT</mml:mi>mml:mrowmml:mia</mml:mi>mml:mo,</mml:mo>mml:mib</mml:mi></mml:mrow></mml:msub></mml:math></jats:alternatives></jats:inline-formula> with parameters jats:italica</jats:italic>, jats:italicb</jats:italic> such that jats:italicab</jats:italic> is a root of a Littlewood polynomial, there exist large level sets. As a consequence, we show that for some parameters jats:italica</jats:italic>, jats:italicb</jats:italic>, the Assouad dimension of graphs of jats:inline-formulajats:alternativesjats:tex-math$$T_{a,b}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:msubmml:miT</mml:mi>mml:mrowmml:mia</mml:mi>mml:mo,</mml:mo>mml:mib</mml:mi></mml:mrow></mml:msub></mml:math></jats:alternatives></jats:inline-formula> is strictly larger than their upper box dimension. In particular, we can find weak tangents of those graphs with large Hausdorff dimension, larger than the upper box dimension of the graphs.</jats:p>