In this lesson, Function Petting Zoo, our instructor Vincent Selhorst-Jones gives an introduction on a variety of functions. Youll get the chance to pet various functions such as the constant function, the identity function, the square function, the cub function, the square root function, the reciprocal function, the absolute function, and the trigonometric function. Exponential and Logarithmic functions, as well as, transformations and compositions are taught. The lesson concludes with four fully worked out examples for extra practice.
An important step in learning mathematics is becoming accustomed to how various functions behave and what their graphs looks like. While long-term experience is the surest way to familiarize yourself with functions, this lesson will help give you a head-start
on developing your "function intuition".
Other teachers or books might call a similar lesson a Function Library or Parent Functions. The point is the same, though: to introduce/review a wide variety of fundamental functions, along with their characteristics and graphs.
As we work through these functions and see their graphs, don't forget: axes matter. Pay attention to the "graphing window" so you can interpret what you're seeing. For the majority of these graphs, we'll use x: [−10, 10], y: [−10,
10], but a few graphs will be different.
We can't really explain or show the graphs here in the notes, so make sure to check out the video if you need to familiarize yourself with these fundamental functions. Here is a list of the functions we examine in this lesson:
The Constant Function: f(x) = k
The Identity Function: f(x) = x
The Square Function: f(x) = x2
The Cube Function: f(x) = x3
The Square Root Function: f(x) = √x
The Reciprocal Function: f(x) = 1/x
The Absolute Value Function: f(x) = |x|
The Trigonometric Functions: f(x) = sin(x) & g(x) = cos(x)
The Exponential and Logarithmic Functions: f(x) = 10x & g(x) = log10(x)
Function Petting Zoo
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.