Question

F(x)= (2x^2 +5x−12)/(x^2 −3x−28)

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Does this graph have point, infinite, or jump discontinuity? Or two, if so which two?
Option 1: Point discontinuity at x = 7.
Option 2: Infinite discontinuity at x = 4 and x = -7.
Option 3: Jump discontinuity at x = 4 and x = 7.
Option 4: Point discontinuity at x = -4.

Answer 1

The graph of the given function has point discontinuity at x = -4.

Step-by-step explanation:

The given function is f(x) = (2x^2 + 5x - 12)/(x^2 - 3x - 28). To determine the type of discontinuities, we need to check if there are any values of x that cause the denominator to equal zero. Setting the denominator equal to zero, we get (x - 7)(x + 4) = 0. So, x can be 7 or -4. Now, we need to check the behavior of the function as x approaches these values.

When x approaches 7, the function has a point discontinuity since the numerator does not approach infinity and the denominator approaches zero. Similarly, when x approaches -4, the function also has a point discontinuity. Therefore, the correct option is Option 4: Point discontinuity at x = -4.