Consider the functions $f$ and $g$ defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad \text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]ex plain why $f$ and $g$ are not the same function.

Two corresponding sides of two similar triangles are 3cm and 5cm. the area of the first triangle is 12cm^2. what is the area of the second triangle?

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.

Afarmer has 5 times as many cows as pigs. the farmer only has cows and pigs, and he has 168 animals. how many cows does he have?