## anonymous one year ago Which of the following functions is continuous at x = 3?

1. anonymous

A. B. C. D

2. anonymous

D.all are continuos at x = 3

3. Michele_Laino

hint: the subsequent function: $\Large f\left( x \right) = \frac{{{x^2} - 9}}{{x + 3}}$ is continuous at the subsequent set: $\Large \left\{ {x \in {\mathbf{R}},\quad x \ne - 3} \right\}$

4. Haseeb96

5. anonymous

isint c right too though?

6. Haseeb96

no

7. UsukiDoll

Ah. I thought I misunderstood this. nevermind XD But yeah don't pick functions that are fractions because it causes restrictions and discontinuity.

8. UsukiDoll

I'll demonstrate why A is correct... |dw:1438416902248:dw| use difference of square formula for the numerator

9. UsukiDoll

|dw:1438416939205:dw| cancel out the x +3. Your new function is f(x) = x-3 and it's not a fraction, so all reals.

10. UsukiDoll

B and C are knocked out... for 2 reasons 1. piecewise function 2. jump discontinuity or point discontinuity is present in the graph. discontinuity occurs when there is asymptotic discontinuity there are gaps also known as jump discontinuity, or a hole is present (point discontinuity) .