Question

suppose that the function \\(f\\) is defined, for all real numbers, as follows.

\\f(x) = \

$$\begin{cases} 2x - 1 & \\text{if } x < 1 \\\\ -x + 2 & \\text{if } x \\ge 1 \\end{cases}$$

\\

graph the function \\(f\\). then determine whether or not the function is continuous.

is the function continuous?
yes
no

Explanation:

Evaluate the left-hand limit at the boundary

$$ \lim_{x \to 1^-} f(x) = \lim_{x \to 1^-} (2x - 1) = 2(1) - 1 = 1 $$

Evaluate the right-hand limit and function value at the boundary

$$ f(1) = \lim_{x \to 1^+} f(x) = \lim_{x \to 1^+} (-x + 2) = -1 + 2 = 1 $$

Determine continuity and identify key plotting points

$$
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$$

Answer:

Is the function continuous?

• Yes (Correct answer)
• No