Question

[10 Points] Determine whether the function $f(x) = egin{cases} x^2 - 4x & \text{if } x \le -2\\ \frac{-30x}{x^2 + 1} & \text{if } -2 < x < -1\\ 4x + 1 & \text{if } x > -1 \end{cases}$ is continuous/discontinuous at $x = -2, -1, 1$. For each discontinuity, identify its type.

          [10 Points] Determine whether the function
$f(x) = egin{cases} x^2 - 4x & \text{if } x \le -2\\ \frac{-30x}{x^2 + 1} & \text{if } -2 < x < -1\\ 4x + 1 & \text{if } x > -1 \end{cases}$
is continuous/discontinuous at $x = -2, -1, 1$. For each discontinuity, identify its type.

[10 Points] Determine whether the function
f(x) = egincases x^2 - 4x if x ≤ -2
(-30x)/(x^2 + 1) if -2 < x < -1
4x + 1 if x > -1
is continuous/discontinuous at x = -2, -1, 1. For each discontinuity, identify its type.

Added by Amy H.

Calculus: One Variable

Garret J. Etgen, Saturnino L. Salas 10th Edition

Chapter 2

Instant Answer

Solved by Expert Linda Winkler

Step 1

To determine if the function is continuous at x = -2, we need to check if the left-hand limit and the right-hand limit exist and are equal. The left-hand limit as x approaches -2 is given by lim(x->-2-) f(x) = lim(x->-2-) (x^2 - 4x) = (-2)^2 - 4(-2) = 4 + 8 = Show more…

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Determine whether the function f(x) = x^2 - 4x if x â‰¤ -2 f(x) = -1 if -2 < x â‰¤ -1 f(x) = x^2 + 1 if -1 < x â‰¤ 1 f(x) = 4x + 1 if x > 1 is continuous/discontinuous at x = -2, -1, 1. For each discontinuity, identify its type.