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I just wanted to say good job for providing a positive feedback to peer, definition, steps, and visuals! I will provide you math sentence frames in future! You can also "comment" under a post.

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Great job with your accurate example and detailed description and steps
-Helene Hahn

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f(x)=f(-x) the graph is reflected over the y axis

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compact and informative, how nice summary of zeros is :)
- Jeongrok Bae

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Even function: one of the functions that the value of x does not change even though -x is put into x-value.

ex:

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Very well drawn graph and accurate definition. :)

-Jenna Anderson

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Horizontal Asymptote:
One or more horizontal lines that a graph approaches but never crosses.

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Your definition is clear and your graph provides an excellent and easily understandable visual. :)

-Jenna Anderson

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Vertical Asymptote Behavior:
The behavior of a function as it approaches the vertical asymptote, a vertical line that the graph will never cross.

Depending on if the graph is approaching the VA on the left or right side you need to specify by including a positive (for right) or negative (for left) sign in the VA behavior for x.

For the graph below the vertical asymptote behavior is:
lim x -> 1+
f(x) -> + infinity

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Zeros
Points where the graph of a function cross the x-axis

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Your clear and easy to understand definition of bounded below with the visual example helped me understand how it is applied to a graph. - Hailey Moon

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Inverse Function - a function that if “f” is applied to an input of x it will give a result of y. An inverse function is reflected across the graph of y=x from the original function.

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You have a clear and concise definition that is to the point and an easy example that helped me understand the concept immediately.

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Bounded Below
A function that is bounded below creates a graph that continues infinitely above the vertex or some (imaginary) horizontal line.

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your description and example of end behavior helped me understand the concept better:) -kelly yoon

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good definition for even functions and clear example :)

-Joanne Kim

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Hole:
occurs when denominator is zero, but has common factor for denominator and numerator

y=(2x+1)(x-2) /(x-2)

hole at x=2

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Bounded Above:
The function has a range limit somewhere before positive infinity, stopping at a defined y coordinate, while the range also goes to negative infinity.

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Even Function
A function is even if it is symmetrical to the y-axis.
Can check it algebraically
by f(x)=f(-x)

For example:
f(x)=x²+2
f(-x)=(-x)²+2=x²+2
f(x)=f(-x)
it is a even function

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Good concise answer, with a very good graphic

Elliot Chun

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Domain - The set of all points for any given function such that the function is defined.

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Hole, vertical asymptote, horizontal asymptote, zeros, y-intercept, domain, range, even function, odd function, composition function, inverse function, symmetry respect to origin, symmetry respect to y-axis, bounded above, bounded below, end behavior, vertical asymptote behavior, difference quotient, explicit equation, implicit equation, one-to-one function

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Your definition was clear and easy to follow. I like that you gave an example and drew the graph! -Olivia Anaya

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Great definition with a clear graph.

-Brandon Kimes

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Inverse function- A function that is derived from a given function by interchanging the two variables. F(x) = y.

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Good explanation on symmetry respect to the origin. It was easy to understand and the graph you drew does a good job at showing an example of your explanation.
-Jacob Lee

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Good definition, and thanks for adding the equation to test it. By the way, it is spelled algebraically. :D
By Lynette Jeong

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Your example is very easy to follow and it helped me better understand how to find where the hole is at.  -Garrett Brookman

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Hole - A hole is a removable discontinuity or removable singularity.

If the same factor is in the numerator and denominator in the lowest terms possible, there is a hole.

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A hole occurs when the denominator is zero but has a common factor for denominator and numerator.

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Nice example, graph is clear and able to understand
-Caitlyn Chou

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Your definition was easy to understand and gave a clear explanation of what domain is. The example also did a good job of building onto the concept. -Paris Luna

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Your definition on bounded above gave me a better understanding on how a graph can be restricted below a point.
-Jason Yoon

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Your response was easy to understand and provided a good example about setting y=0. I know now that zeros hit the x-axis - By Josh Han

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Symmetry Respect to Origin
When a graph is symmetric to both x and y axis. The graph looks the same right side up and upside down.

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Gives a clear understanding of how the range in a function are all the y values possible in a function.
- Joseph Park

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That was a good example that gave me an understanding on inverse functions.
- Jinny Shim

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Symmetry respect to y-axis- a function that can be folded across the y-axis so the two halves match

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Your response was clear cut and helps give an understanding what bounded below means.
-mark m.

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Bounded above - when the function has an absolute maximum and no other points go above it. This means the function can only go down from there.

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End behavior: The end behavior of the polynomial function is the behavior of the given graph of f (x) as x approaches positive or negative infinity. The coefficient and the degree determines the end behavior of the graph. For example: We would look at the right of the x-axis and as x approaches positive infinity. To the left of the x-axis as x approaches negative infinity.

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Range - All the y values possible in a function.
Ex. The range of y=x is all real numbers.

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Bounded Below - When a function has an absolute minimum and all other points of that function cannot go lower than that point.

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Y-intercept - The point on the graph where the x=0. There can only be one for it to be a function. You can check it algebraically by checking what f(0) =

Examples:
f(0)= 2(0)^2 - 4(0) + 8 = 8
f(0)= 4(0) - 9 = -9

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The DOMAIN of a function is the set of all possible x-values or inputs that will make the function work, and output a real y value.
For example, the domain of the graph below is all real numbers or (-oo, oo)

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inverse function: An inverse function is the opposite of a function. You switch the x and y and solve for the y.
example: f(x)=2x+1 —> f^-1(x)=x-1/2
feedback: if there is a given point such as (3,1) you just switch the x and y to find the inverse which will be (1,3)

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End behavior-a function is the behavior of the graph of the function  f(x) as x approaches positive infinity or negative infinity.
Example show:
as x approaches +∞, f(x) approaches  +∞.
as x approaches −∞, f(x) approaches  −∞.

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even function - a function that has symmetry respect to the
y-axis. It can be checked algebraically if f(-x) is the same as f(x).

Examples:
f(x)= -x^2 + 6
f(-x)= -(-x)^2 +6
f(-x)= -x^2 + 6

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Odd function- the odd function is a graph that is symmetric with respect to the origin. to check algebraicly, f(-x)= - f(x)
EX:
f(x) = -8/x
f(-x) = -8/-x
f(-x) = 8/x

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The zeros are your x intercept.  To find the zeros you set y=0 and then you solve for x.