Original vs. Transformed Function Graphs

The function $f(x) = rac{1}{x^2 + 1}$ is transformed to obtain the function $g(x) = rac{a}{(x-b)^2 + 1} + c$, where $a$, $b$, and $c$ are re…

The function $f(x) = e^x$ is transformed by a vertical dilation of factor $a$, where $a > 0$, followed by a reflection in the $x$-axis, and…

The graph of $y = f(x)$ is transformed to obtain the graph of $y = f(x+3) - 2$. State the geometric transformations that map the graph of $y…