Mathematics

Problem

Determine the value of

a

that makes the function

f(x)= \begin{cases} x^{2}-4, & x<1\\ ax+1, & x\ge 1 \end{cases}

continuous at

x=1

. a)

a=2

a=4

a=-4

a=-3

Intuitive explanation

Continuity at a point requires that the left and right limits match the function value there. Here, you need the parabola approaching from the left to "meet" the linear piece coming from the right at $x=1$ . Find what value the left piece approaches as $x \to 1^-$ , then set the right piece equal to that same output—this single equation in $a$ is your answer.

Intuitive explanation

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