Notes
Domain: All Possible x values
Range: All Possible y values
| \({\text{Domains of Special Functions}}\) |
| \(\underline{\text{Type}}\) |
\(\underline{\text{Parent Function}}\) |
\(\underline{\text{Domain}}\) |
| \(\text{Denominator}\) |
\(f(x)=\displaystyle\frac{1}{x}\) |
\(x \ne 0\) |
| \(\text{Square Root}\) |
\(f(x)=\sqrt{x}\) |
\(x \ge 0\) |
| \(\text{Square Root in Denominator}\) |
\(f(x)=\displaystyle\frac{1}{\sqrt{x}}\) |
\(x \gt 0\) |
Practice Problems
State the Domain of each function.
\(\textbf{1)}\) \(f(x)=\displaystyle\frac{3}{x-5}\)
Domain: \((-\infty ,5)\cup(5,\infty)\,\,\,\) or \(\,\,\,x\ne5\)
\(\textbf{2)}\) \(f(x)=\displaystyle\frac{3}{x^2-6x+8} \)
Domain: \((-\infty,2)\cup(2,4)\cup(4,\infty)\,\,\,\) or \(\,\,\,x\ne2,4 \)
\(\textbf{3)}\) \(f(x)=\displaystyle\sqrt{x-4} \)
Domain: \([ 4,\infty)\,\,\, \) or \(\,\,\, x\ge4\)
\(\textbf{4)}\) \(f(x)=\displaystyle\sqrt{5-3x} \)
Domain: \(\left( -\infty,\frac{5}{3}\right]\,\,\,\) or \(\,\,\, x\le\frac{5}{3}\)
\(\textbf{5)}\) \(f(x)=\displaystyle\sqrt{x^2-4}\)
Domain: \(( -\infty,-2]\cup[ 2,\infty) \,\,\,\) or \(\,\,\, x \le -2 \cup x \ge 2 \)
\(\textbf{6)}\) \(f(x)=\displaystyle\frac{\sqrt{5}}{\sqrt{x+3}} \)
Domain: \((-3,\infty)\,\,\,\) or \(\,\,\, x>-3 \)
\(\textbf{7)}\) \(f(x)=\displaystyle\frac{2x+5}{\sqrt{2-4x}} \)
Domain: \( \left(-\infty,\frac{1}{2} \right)\,\,\, \) or \(\,\,\, x\lt \frac{1}{2} \)
\(\textbf{8)}\) \(f(x)=\displaystyle\frac{x+14}{1-e^x} \)
Domain: \((-\infty,0)\cup(0,\infty) \,\,\,\) or \( \,\,\, x\ne0 \)
\(\textbf{9)}\) \(f(x)=\displaystyle\frac{x^2+4}{e^{cos(x)}} \)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
\(\textbf{10)}\) \(f(x)=x+2\)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
\(\textbf{11)}\) \(f(x)=\displaystyle \frac{x+2}{3}\)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
\(\textbf{12)}\) \(f(x)=4x+\sqrt{2}\)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
\(\textbf{13)}\) \(f(x)=\displaystyle \frac{x+2}{\sqrt{3}}\)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
\(\textbf{14)}\) \(f(x)=x^2+5\)
Domain: \((-\infty,\infty) \,\,\, \) or \(\,\,\,\) All Real Numbers
See Related Pages\(\)
