Natural Exponential Graphs

Natural Exponential Graphs

$\textit{Natural Exponential Graphs}$ $$y=e^x$$ Natural Exponential Graphs also follow the rule of translations and transformations. Example 1 Sketch the graphs of $y=e^x$ and $y=-e^x$. Show Solution Reflected to the $x$-axis. Example 2 Sketch the graphs of $y=e^x$ and $y=-e^{-x}$. Show Solution Example 3 Sketch the graphs of $y=e^x$ and $y=e^{-x}$. Show Solution Example 4 Sketch [...]
Cubic Graph Sketching

Cubic Graph Sketching

Basics of Cubic Graph Sketching Cubic Graph Sketching start considering from the \(x\)-intercepts and whether the leading coefficient is either positive or negative. Question 1 Sketch the graph of \( y=(x-1)(x+2)(x-3) \). Show Solution Question 2 Sketch the graph of \( y=(x^2-2x)(x+3) \). Show Solution \( y=(x^2-2x)(x+3) = x(x-2)(x+3) \) Question 3 Sketch the graph [...]