Topics:
• Basic graphs: the graphs of the following functions are essential to know:
Important feature: this graph has an inflection point (the s-curve) at (0,0)
Important feature: the domain is only the interval
Important feature: the graph approaches the lines x=0 and y=0 (the two coordinate axes). These lines are called asymptotes. Notice that x=0 is not in the domain.
• Transformations of graphs:
vertical translation (shift) – add a number to the output (value of the function)
horizontal translation (shift) – add a number to the input
vertical stretching or squeezing – multiply the output by a positive number
horizontal stretching or squeezing – multiply the input by a positive number
reflection in the x-axis – multiply the output by -1
reflection in the y-axis – multiply the input by -1
• Even and odd functions:
Basically, even functions have graphs which have the same symmetry as the graph of 
Algebraic tests:
A function is even if and only if 
A function is odd if and only if 
Homework:
• Reread/ review all the examples, making sure that you see how the transformations change the graphs (and why!) and how the algebraic test for an even or odd function checks the symmetry. You can use Piazza to discuss if you have questions.
• Do the assigned problems from Session 5
• No WeBWorK or Warm-Up today because we have class tomorrow!
• Don’t forget Test 1 Review
