Given:
Given that the function [tex]p(x)=\left\{\begin{array}{ll}\frac{1}{4} x^{2}+1 & \text { if } x \leq 3 \\\frac{1}{4} x+2.5 & \text { if } x>3\end{array}\right.[/tex]
We need to determine the function to evaluate when x = -5.
Function:
The function is given two interval. The interval [tex]x\leq 3[/tex] means that x takes all values less than or equal to 3.
And the interval [tex]x>3[/tex] means that x takes all values greater than 3.
We need to determine the function that takes the limit when x = -5.
From the two limits, the limit x = -5 lie in the interval [tex]x\leq 3[/tex] because the interval takes all x values less than or equal to 3.
Hence, the function is [tex]p(x)=\frac{1}{4} x^{2}+1[/tex]
Thus, Option A is the correct answer.
