Graphs and Special Functions

Name: Graphs and Special Functions
Author: StemPy Lab

A picture of a function tells you in a moment what a formula hides. In this course we read and draw the graphs of the common functions, we meet the modulus and the greatest integer function, and we learn how to move, stretch and flip a graph. We also learn to see even, odd, increasing and decreasing functions in a picture.

4 lessons, about 1 h 40 min4 simulations16 problems8 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (4 lessons)

Lesson 1about 25 min
Reading and drawing graphs
The graph of a function f is the set of points (x, f(x)). We draw it from a table of values and we read domain, range, zeros and the value at a point from it. The six standard graphs are $y = x$ , $x^2$ , $x^3$ , $\frac{1}{x}$ , $\sqrt{x}$ and $\frac{1}{x^2}$ . The graph of $y = ax^2 + bx + c$ is a parabola with its vertex at $x = -\frac{b}{2a}$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 2about 25 min
The modulus, the greatest integer and other special functions
The modulus |x| is the distance of x from zero. The signum gives the sign of x. The greatest integer [x] is the largest integer not more than x, and the fractional part is x − [x], which always lies in [0, 1). A function defined by different rules on different parts of its domain is a piecewise function.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Moving, stretching and flipping a graph
Adding a number outside f moves the graph up or down. Changing x inside f moves or squeezes it sideways, and the effect is the opposite of what you may expect. A factor outside stretches the graph up or down. A minus sign outside flips it in the x axis, and a minus sign inside flips it in the y axis.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 4about 25 min
Even, odd, increasing and decreasing functions
A function is even if f(−x) = f(x) for every x, and then its graph is symmetric about the y axis. It is odd if f(−x) = −f(x), and then its graph is symmetric about the origin. A function is increasing on an interval if a larger x always gives a larger f(x), and decreasing if a larger x gives a smaller f(x). A function is periodic with period T if f(x + T) = f(x).
1 simulation2 practice questions1 Python program4 problems1 question set1 note
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Graphs and Special Functions: Timed Test

20 questions · 50 min

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Graphs and Special Functions

Course outline (4 lessons)

Reading and drawing graphs

The modulus, the greatest integer and other special functions

Moving, stretching and flipping a graph

Even, odd, increasing and decreasing functions

Test Your Learning

Your teacher

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