Graphing
Where MATH is drawn to VISUALIZE
R-Rated
You can't be
here, or there
DOMAIN & RANGE
Think of the modes of transport you had when growing up and how far you travelled with that mode. Your DOMAIN was controlled by your area. RANGE depended on your vehicle.
1 yr old - Walker moves around a room
2 yr old - Tricycle rolled around the driveway
3 yr old - Bicycle rode to the park
Tween - bus pass gets you to the mall
16 yr old - Car gets you all over town
TRAVEL BEYOND THESE LIMITS IS RESTRICTED
How do we write this in math is through use of brackets,
either ( ), [ ], ( ],[ )
Round parenthesis do not include the end number, square brackets include the last number.
Think of the Square Brackets as a container so it includes everything in it, and Round Brackets as an overflowing bag that bulges and does not hold everything.
IMPORTANT when using infinity you can NEVER contain it so always use Round Brackets!
Almost, Not Quite or High School Crush.
What are Asymptotes? If I never meet one how would I know who they are?
Imagine travelling to the moon as a crew of four with two landing on the moon and two staying in lunar orbit. The two astronauts in the lunar orbiter travelled 400,000 plus kilometers to not take a single step on the moon. It would be hard to find a better definition of almost, but they are flying the function/path very close to the surface without actually touching it.
I can only imagine the professional jealousy on the return flight.
DISCLAIMER: Sorry to the Artemis IV crew in advance for any squabbles I may have caused.
VLT - IF! I could Turn Back TIME
Why can a function not cross a vertical line?
Remember the definition of a function is it has one and only one unique solution for each input. Translating this to an equation on the Cartesian plan there is only one y-value for each x-value.
Recall the y-axis is the DEPENDENT axis while the x-axis is the INDEPENDENT axis. As x changes y will depending on where x is. The most independent variable to think of is time and is placed on the x-axis.
Time can only progress forward, we cannot go back, so there is no opportunity for it to come back to a lesser x-value. This condition makes it impossible to cross a vertical line, hence the VLT.