  We provide upper bounds for the Assouad spectrum
$\dim_A^\theta(\text{Gr}(f))$ of the graph of a real-valued H\"older or Sobolev
function $f$ defined on an interval $I \subset \mathbb{R}$. We demonstrate via
examples that all of our bounds are sharp. In the setting of H\"older graphs,
we further provide a geometric algorithm which takes as input the graph of an
$\alpha$-H\"older continuous function satisfying a matching lower oscillation
condition with exponent $\alpha$ and returns the graph of a new
$\alpha$-H\"older continuous function for which the Assouad $\theta$-spectrum
realizes the stated upper bound for all $\theta\in (0,1)$. Examples of
functions to which this algorithm applies include the continuous nowhere
differentiable functions of Weierstrass and Takagi.
