Question

Which function should be used to when evaluating the function at x = −5? HELP ASAP!!

Answer 1

Given:

Given that the function $p(x)=\left\{\begin{array}{ll}\frac{1}{4} x^{2}+1 & \text { if } x \leq 3 \\\frac{1}{4} x+2.5 & \text { if } x>3\end{array}\right.$

We need to determine the function to evaluate when x = -5.

Function:

The function is given two interval. The interval $x\leq 3$ means that x takes all values less than or equal to 3.

And the interval $x>3$ 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 $x\leq 3$ because the interval takes all x values less than or equal to 3.

Hence, the function is $p(x)=\frac{1}{4} x^{2}+1$

Thus, Option A is the correct answer.