Question

sketch the graph and find the x-values (if any) at which f is not

continuous. Classify the discontinuities as being removable or essential. If the latter, state

whether it is a jump discontinuity, an infinite discontinuity, or neither.

Step 1

Let's examine the numerator

x^{2} + 7x + 10 = x^{2} + 2x + 5x + 10 = x(x+2) + 5(x+2) = (x+2)(x+5)

hence the given function is actually (x+2) in the simple form. Hence it's a continuous function exverywhere except at x where deominator is zero.

Step 2

Denominator: x+5 = 0 when x = -5.

At x=-5, the function doesn't exist.

Hence there is no question of continuity at x = -5.

Step 3

So, the answer to the first part is:

1. The graph is identical to the graph of a linear function f(x) = x + 2 except at x = -5 where the function d...

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