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If a function h (x) is given by h (x)= {x^2 + x - 12, if x less than or equal to 1: 3 - x, if x...

Question:

If a function {eq}h (x) {/eq} is given by {eq}h(x)= \begin{cases} x^2 + x - 12, &\text{if}\ x \le 1\\ 3 - x, &\text{if}\ x \gt 1 \end{cases} {/eq}.

(a) Draw graph of {eq}h (x) {/eq}.

(b) Determine whether {eq}h (x) {/eq} is continuous or discontinuous at {eq}x = 1 {/eq}.

Continuity of Function:

A function of one real variable {eq}f(x) {/eq} is continuous at any point if, for every value {eq}a {/eq}, the left and right limits

of the function are finite and equal

{eq}\displaystyle \lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x). {/eq}

Answer and Explanation:

We are given the piecewise function

{eq}h(x)= \begin{cases} x^2 + x - 12, &\text{if}\ x \le 1\\ 3 - x, &\text{if}\ x \gt 1 \end{cases} {/eq}.

(a...

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Continuity in a Function

from Math 104: Calculus

Chapter 2 / Lesson 1
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