# Graphing Logarithmic Functions

The inverse function of $y=a^x$ is $y=\log_{a}{x}$. Therefore $y=\log_{a}{x}$ is an inverse function, it is a reflection of $y=a^x$ in the line $y=x$. The graphs of $y=a^x$ is $y=\log_{a}{x}$ for $0 \lt a \lt 1$: The graphs of $y=a^x$ is $y=\log_{a}{x}$ for $a \gt 1$: \begin{array}{|c|c|c|} \require{color} \hline & y=a^x & \color{red}y =\log_{a}{x} \\ \hline […]

# Natural Exponential Graphs

$$y=e^x$$ Natural Exponential Graphs also follow the rule of translations and transformations. Example 1 Sketch the graphs of $y=e^x$ and $y=-e^x$. Reflected to the $x$-axis. Example 2 Sketch the graphs of $y=e^x$ and $y=-e^{-x}$. Example 3 Sketch the graphs of $y=e^x$ and $y=e^{-x}$. Example 4 Sketch the graphs of $y=e^x$ and $y=e^{x+1}$. Translated to left. […]

# Exponential Graphs

Functions of the form exponential, where the base is a positive real number other than 1 are called exponential graphs or exponential functions.

# Quartic Graph Sketching

Quartic Graph Sketching is based on their concavities and x-intercepts to determine the basic shape of the quartic graphs. Question 1 of Quartic Graph Sketching Sketch the graph of $y=(x-1)(x+1)(x+2)(x-3)$. Question 2 Sketch the graph of $y=x(x^2-x)(x-2)(x+3)$. $=x(x-1)(x-2)(x+3)$ Question 3 Sketch the graph of $y=x^2(x-3)(x+3)$. Question 4 […]