Review of Exponential Functions $y=b^x$

Review of Exponential Functions y = bx

• $f\left(x\right)$ has a horizontal asymptote at $y=0$
• The y-intercept is $\left(0,\ 1\right)$
• Domain: $x\in R$; Ranage $y>0$

• $\boxed{y=\log_bx\ \ \ \leftrightarrow\ \ \ x=b^y}$
• $\boxed{b^{\log_bx}=x}$ and $\boxed{\log_b\left(b^x\right)=x}$
• The x-intercept is $\left(1,\ 0\right)$
• Domain: $x>0$; Range: $y\in R$
• It has a vertical asymptote at $x=0$

Review of Exponential Rules

• $\displaystyle a^{\orange{x}}\cdot a^{\green{y}}=a^{\orange{x}+\green{y}}$
• $\displaystyle \frac{a^{\orange{x}}}{a^{\green{y}}}=a^{\orange{x}-\green{y}}$
• $\displaystyle \left(a^{\orange{x}}\right)^{\green{y}}=a^{\orange{x}\green{y}}$
• $\displaystyle \left(a\cdot b\right)^{\orange{x}}=a^{\orange{x}}\cdot b^{\orange{x}}$
• $\displaystyle \left(\frac{a}{b}\right)^{\orange{x}}=\frac{a^{\orange{x}}}{b^{\orange{x}}}$