Exponential Function.
\begin{equation*}
f(x) = ab^x,~~~~ \text{ where } ~~~b \gt 0 ~~~\text{ and } ~~~b \ne 1 \text{, } ~~~a \ne 0
\end{equation*}
\(x\) | \(f(x)\) |
\(-3\) | \(\frac{1}{8}\) |
\(-2\) | \(\frac{1}{4}\) |
\(-1\) | \(\frac{1}{2}\) |
\(0\) | \(1\) |
\(1\) | \(2\) |
\(2\) | \(4\) |
\(3\) | \(8\) |
\(x\) | \(g(x)\) |
\(-3\) | \(8\) |
\(-2\) | \(4\) |
\(-1\) | \(2\) |
\(0\) | \(1\) |
\(1\) | \(\frac{1}{2}\) |
\(2\) | \(\frac{1}{4}\) |
\(3\) | \(\frac{1}{8}\) |
\(x\) | \(f(x)\) | \(g(x)\) |
\(-2\) | \(\dfrac{1}{9}\) | \(\dfrac{1}{16}\) |
\(-1\) | \(\dfrac{1}{3}\) | \(\dfrac{1}{4}\) |
\(0\) | \(1\) | \(1\) |
\(1\) | \(3\) | \(4\) |
\(2\) | \(9\) | \(16\) |
\(\hphantom{General formula and m}\) |
Power Functions |
Exponential Functions |
General formula |
\(h(x)=kx^p\) |
\(f(x)=ab^x\) |
Description |
variable base and constant exponent |
constant base and variable exponent |
Example |
\(h(x)=2x^3\) |
\(f(x)=2(3^x)\) |
\(x\) | \(h(x)=2x^3\) | \(f(x)=2(3^x)\) |
\(-3\) | \(-54\) | \(\dfrac{2}{27}\) |
\(-2\) | \(-16\) | \(\dfrac{1}{4}\) |
\(-1\) | \(-2\) | \(\dfrac{2}{3}\) |
\(0\) | \(0\) | \(2\) |
\(1\) | \(2\) | \(6\) |
\(2\) | \(16\) | \(18\) |
\(3\) | \(54\) | \(54\) |
\(x\) | \(y=2^x\) | \(f(x)\) | \(g(x)\) |
\(-2\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(-1\) | \(\) | \(\) | \(\) |
\(0\) | \(\) | \(\) | \(\) |
\(1\) | \(\) | \(\) | \(\) |
\(2\) | \(\) | \(\) | \(\) |
\(x\) | \(y=3^x\) | \(f(x)\) | \(g(x)\) |
\(-2\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(-1\) | \(\) | \(\) | \(\) |
\(0\) | \(\) | \(\) | \(\) |
\(1\) | \(\) | \(\) | \(\) |
\(2\) | \(\) | \(\) | \(\) |
\(x\) | \(y=3^x\) | \(f(x)\) | \(g(x)\) |
\(-2\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(-1\) | \(\) | \(\) | \(\) |
\(0\) | \(\) | \(\) | \(\) |
\(1\) | \(\) | \(\) | \(\) |
\(2\) | \(\) | \(\) | \(\) |
\(x\) | \(y=2^x\) | \(f(x)\) | \(g(x)\) |
\(-2\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(-1\) | \(\) | \(\) | \(\) |
\(0\) | \(\) | \(\) | \(\) |
\(1\) | \(\) | \(\) | \(\) |
\(2\) | \(\) | \(\) | \(\) |
\(x\) | \(y\) |
\(0\) | \(3\) |
\(1\) | \(6\) |
\(2\) | \(12\) |
\(3\) | \(24\) |
\(4\) | \(48\) |
\(t\) | \(P\) |
\(0\) | \(0\) |
\(1\) | \(0.5\) |
\(2\) | \(2\) |
\(3\) | \(4.5\) |
\(4\) | \(8\) |
\(x\) | \(N\) |
\(0\) | \(0\) |
\(1\) | \(2\) |
\(2\) | \(16\) |
\(3\) | \(54\) |
\(4\) | \(128\) |
\(p\) | \(R\) |
\(0\) | \(405\) |
\(1\) | \(135\) |
\(2\) | \(45\) |
\(3\) | \(15\) |
\(4\) | \(5\) |
\(t\) | \(y\) |
\(1\) | \(100\) |
\(2\) | \(50\) |
\(3\) | \(33\frac{1}{3} \) |
\(4\) | \(25\) |
\(5\) | \(20\) |
\(x\) | \(P\) |
\(1\) | \(\frac{1}{2} \) |
\(2\) | \(1\) |
\(3\) | \(2\) |
\(4\) | \(4\) |
\(5\) | \(8\) |
\(h\) | \(a\) |
\(0\) | \(70\) |
\(1\) | \(7\) |
\(2\) | \(0.7\) |
\(3\) | \(0.07\) |
\(4\) | \(0.007\) |
\(t\) | \(Q\) |
\(0\) | \(0\) |
\(1\) | \(\frac{1}{4} \) |
\(2\) | \(1\) |
\(3\) | \(\frac{9}{4} \) |
\(4\) | \(4\) |
\(x\) | \(f(x)=x^2\) | \(g(x)=2^x \) |
\(-2\) | ||
\(-1\) | ||
\(0\) | ||
\(1\) | ||
\(2\) | ||
\(3\) | ||
\(4\) | ||
\(5\) |
\(x\) | \(f(x)=x^3\) | \(g(x)=3^x \) |
\(-2\) | ||
\(-1\) | ||
\(0\) | ||
\(1\) | ||
\(2\) | ||
\(3\) | ||
\(4\) | ||
\(5\) |
\(t\) | \(3.5\) | \(4\) | \(8\) | \(10\) | \(15\) |
\(f(t)\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) |