CPM Homework Help : PC Problem 2-146

Given the function $f ( x ) = \left\{ \begin{array} { l l } { x ^ { 2 } + a } & { \text { for } x \leq 1 } \\ { - 2 a x + 7 } & { \text { for } x > 1 } \end{array} \right.$ , what must the value of $a$ be so that $y=f(x)$ is continuous at $x=1$ ? (You can draw it without lifting your pencil.) Try this using the 2-146 HW eTool (Desmos).

Visualize this set of functions using the eTool below.

Hint:

Set the two parts of the function equal to each other for the value of $x=1$ .

Step 1:

$x^2+1=−2ax+7$ for $x=1$

Step 2:

Substitute $1$ in for $x$ and solve for $a$ .