Question

Suppose that the piecewise function $f$ is defined by $f(x) = \begin{cases} \sqrt{3x+4}, & -\frac{4}{3} < x \le 1 \\ -2x^2 + 5x - 2, & x > 1 \end{cases}$. Determine which of the following statements are true. Select the correct answer below: $f(x)$ is not continuous at $x = 1$ because it is not defined at $x = 1$. $f(1)$ exists, but $f(x)$ is not continuous at $x = 1$ because $\lim_{x \to 1} f(x)$ does not exist. $f(1)$ and $\lim_{x \to 1} f(x)$ both exist, but $f(x)$ is not continuous at $x = 1$ because $\lim_{x \to 1} f(x) \ne f(1)$. $f(x)$ is continuous at $x = 1$.

          Suppose that the piecewise function $f$ is defined by
$f(x) = \begin{cases} \sqrt{3x+4}, & -\frac{4}{3} < x \le 1 \\ -2x^2 + 5x - 2, & x > 1 \end{cases}$.
Determine which of the following statements are true.
Select the correct answer below:
$f(x)$ is not continuous at $x = 1$ because it is not defined at $x = 1$.
$f(1)$ exists, but $f(x)$ is not continuous at $x = 1$ because $\lim_{x \to 1} f(x)$ does not exist.
$f(1)$ and $\lim_{x \to 1} f(x)$ both exist, but $f(x)$ is not continuous at $x = 1$ because $\lim_{x \to 1} f(x) \ne f(1)$.
$f(x)$ is continuous at $x = 1$.

Suppose that the piecewise function f is defined by
f(x) = √(3x+4), -(4)/(3) < x ≤ 1
-2x^2 + 5x - 2, x > 1.
Determine which of the following statements are true.
Select the correct answer below:
f(x) is not continuous at x = 1 because it is not defined at x = 1.
f(1) exists, but f(x) is not continuous at x = 1 because limx → 1 f(x) does not exist.
f(1) and limx → 1 f(x) both exist, but f(x) is not continuous at x = 1 because limx → 1 f(x) f(1).
f(x) is continuous at x = 1.

Added by Jamie M.

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