Tell weather if the following is a continuous or discontinuous at a given point.

Question

CONTINUITY AT A POINT

A. Tell weather if the following is a continuous or discontinuous at a given point.

1. f(x) = 3x² + 2x + 1 at x = -2

2. f(x) = 1/x-2 at x = 2

3. f(x) = x-1/x² -1 at x = 1

4. f(x) = log (x² - 3) at x = 2

5. f(x) = 9x² - 1 at x = 1

Answer 1

1 continuous

2 discontinuity

3 discontinuity

4 continuous

5 continuous

2 and 3 involve division by zero, which is undefined. The graphs are undefinied at the place where x=2 for number 2, and where x=1 for number 3

both 2 and 3 are rectangular hyperbolas with two separate branches. at the given x values, the branches are separate. the graphs go from negative infinity then jump to positive infinity.

1 3x^2 +2x +1 is an upward opening parabola with y intercept = 1. At x=-2, f(x) = y=6

the parabola is continuous at all values of x including x=-2

5 is a similar upward opening parabola, continuous at all x values

4 is log(x^2-3) = log(2^2-3) = log(4-3) = log(1) = 0

it's a function that's continuous for all values of x>sqr3 as that makes f(x) = log(0) for x=sqr3 which is undefined. Any x<sqr3 makes f(x) = log(negative number) which is also undefined.