Let
\(f(x) = \begin{cases} 2x^2 - 3&\text{if } x\le 2, \\ ax + 4 &\text{if } x>2. \end{cases} \)
Find a if the graph of \(y=f(x)\) is continuous (which means the graph can be drawn without lifting your pencil from the paper).
We want to first solve this for a
a(2) + 4 = 2(2)^2 - 3 simplify
2a + 4 = 8 - 3
2a + 4 = 5 subtract 4 from both sides
2a = 1 divide both sides by 2
a = 1/2
Here is the graph : https://www.desmos.com/calculator/6oknzzh6sz
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