Domain and range Knowledge-Based Download PDF

Questions

1. 1.

   What is the domain of the real-valued function $f(x) = \sqrt{\frac{x - 1}{x + 4}}$?

   • A) $(-4, 1]$
   • B) $[-4, 1]$
   • C) $(-\infty, -4] \cup [1, \infty)$
   • D) $(-\infty, -4) \cup [1, \infty)$
2. 2.

   What is the range of the real-valued function $f(x) = \sqrt{16 - x^2} - 3$?

   • A) $[-3, 1]$
   • B) $[-3, 4]$
   • C) $[-4, 1]$
   • D) $[0, 1]$
3. 3.

   What is the range of the real-valued function $f(x) = \frac{6}{x^2 + 3}$?

   • A) $[0, 2]$
   • B) $(0, 2]$
   • C) $[0, 3]$
   • D) $(0, 2)$
4. 4.

   What is the domain of the real-valued function $f(x) = \frac{\sqrt{x + 5}}{x - 2}$?

   • A) $(-5, 2) \cup (2, \infty)$
   • B) $[-5, \infty)$
   • C) $[-5, 2) \cup (2, \infty)$
   • D) $(2, \infty)$
5. 5.

   What is the range of the function $f(x) = -x^2 + 6x - 4$ defined for all real numbers $x$?

   • A) $[5, \infty)$
   • B) $(-\infty, 5]$
   • C) $(-\infty, 3]$
   • D) $[3, \infty)$