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## Algebra 2

### Course: Algebra 2>Unit 12

Lesson 2: Interpreting features of functions

# Symmetry of algebraic models

Sal interprets the significance of modeling function being even. Created by Sal Khan.

## Want to join the conversation?

• in the following questions does anyone know what the term end behavior means?
• Yes, end behavior is how a function behaves as x gets very large (both in the negative and positive direction). The main thing we are interested in is whether f(x) is increasing or decreasing as x grows very large.
For example, f(x) = x² - x + 2 keeps increasing as x gets very large, so its positive end behavior is "increasing" or "upward" (different teachers use different word".
Likewise, when x becomes very negative, this function keeps increasing so its negative end behavior is "increasing" or "upward".

But, f(x) = x³ + 2x² - 3 is different. When x is very negative, it is decreasing or "downward". So its negative (sometimes called left hand) end behavior is downward or decreasing. However, when x if very large on the positive side, f(x) goes up, so its positive or right hand end behavior is increasing or upward.

If you have a good algebra teacher, you will get a slightly more rigorous way of saying the same thing:
Negative side, going down would be written as: f(x)→−∞ as x→−∞
This is read as "f(x) approaches negative infinity as x approaches negative infinity"
Similarly,
Negative side, going up would be written as: f(x)→ + ∞ as x→−∞
Positive side, going down would be written as: f(x)→−∞ as x→ +∞
Positive side, going up would be written as: f(x)→ + ∞ as x→+∞

There is a video on this:
• At , Sal says that T(v) = T(-v) defines the function as even. An odd function is defined as T(v) = -T(-v), right?
• This is not super necessary to say but I just noticed that... Scott, you're right T(v)= -T(-v) but Gene is also right -T(v)=T(-v). Those two statements say the same thing. To convert from one to the other just multiply both sides by -1.
• So magnitude is like absolute value?
• Well, absolute value is a type of magnitude (amount given, but no direction given).
On the other hand, any given integer (signed number) represents a vector (amount and a direction is given). Not sure if that answers your question...
• Did khan academy change their videos to their own? I liked the youtubes
• So any quadratic function who's symmetry is the y axis is even?
EDIT: And any absolute value function who's symmetry is the y axis is even?
(1 vote)
• Any function that is symmetric about the y axis is even, period. It doesn't matter if it's polynomial, trigonometric, or whatever weird thing you can cook up.