请以资深中国数学教师的身份，根据我提供的图片，总结复习对数函数知识点以及重难点，讲解话术要求都用文字呈现出来。要求讲解过程图像和文字合理搭配，用不同的颜色标注，语言风格风趣幽默，简单易懂。---**Knowledge Point:** Knowledge Point Six: Graphs and Properties of Logarithmic Functions **Introduction:** The graph and properties of the logarithmic function $y = \log_a x (a>0, \text{ and } a \neq 1)$ are shown in the table below: **Table:** | Property | $a>1$ | $01$ | $0- Type: Logarithmic function graph.
- Coordinate System: X-axis and Y-axis intersecting at origin O.
- X-axis label: x, positive direction indicated by arrow.
- Y-axis label: y, positive direction indicated by arrow.
- Curve: A curve passing through (1,0), increasing as x increases.
- Label: $y = \log_a x (a>1)$.
- Vertical Line: Dashed line $x=1$. | **Chart Description:**
- Type: Logarithmic function graph.
- Coordinate System: X-axis and Y-axis intersecting at origin O.
- X-axis label: x, positive direction indicated by arrow.
- Y-axis label: y, positive direction indicated by arrow.
- Curve: A curve passing through (1,0), decreasing as x increases.
- Label: $y = \log_a x (0- Vertical Line: Dashed line $x=1$. | | 定义域 (Domain) | $(0, +\infty)$ | $(0, +\infty)$ | | 值域 (Range) | $\mathbb{R}$ | $\mathbb{R}$ | | 单调性 (Monotonicity) | 在 $(0, +\infty)$ 上是增函数 (Is an increasing function on $(0, +\infty)$) | 在 $(0, +\infty)$ 上是减函数 (Is a decreasing function on $(0, +\infty)$) | | 共点性 (Common Point) | 图像过定点 $(1,0)$, 即 $x=1$ 时, $y=0$ (The graph passes through the fixed point $(1,0)$, i.e., when $x=1$, $y=0$) | 图像过定点 $(1,0)$, 即 $x=1$ 时, $y=0$ (The graph passes through the fixed point $(1,0)$, i.e., when $x=1$, $y=0$) | | 函数值 (Function Value) | $x \in (0,1)$时, $y \in (-\infty, 0)$;
$x \in [1, +\infty)$时, $y \in [0, +\infty)$ | $x \in (0,1)$时, $y \in (0, +\infty)$;
$x \in [1, +\infty)$时, $y \in (-\infty, 0]$ | | 特点 (Characteristics) | | | | 对称性 (Symmetry) | 函数 $y=\log_a x$ 与 $y=\log_{\frac{1}{a}} x$ 的图像关于 $x$轴对称 (The graphs of the functions $y=\log_a x$ and $y=\log_{\frac{1}{a}} x$ are symmetric about the x-axis) | |