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# Let Find $a$ if the graph of $y=f(x)$ is continu

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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).

Feb 2, 2018

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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

Feb 2, 2018