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### Course: Algebra 1>Unit 8

Lesson 1: Evaluating functions

# Evaluating discrete functions

Given the graph of a discrete function, Sal shows how to evaluate the function for a few different values.

## Want to join the conversation?

• What makes this function discrete? Why have it in the title but not address it in the video? Just curious.
• The discrete function is based on the visual which has a bunch of points, all the values in between do not count. This is opposed to continuous which is shown by lines so that 1/2s and .343, etc. all can be inputted.
• Which function passes through the points (2, 3) and (4, 4)
• There may be a variety of functions that go through the points, so specify if you want a linear function, quadratic function, absolute value, or what.
• whats a way we would use discrete function in real life.
• You could write an "is a function of" statement and think about it. For example, "total cost" is a function of "*# of shoes*". Then you can plot it, and if you can't buy half of a shoe, then it's discrete. That, or you can't buy more than and x number of shoes.
• you said that y=h(x) is not a function if the graph has 2 y values.
what if the function was x=h(y)
would it be the other way around? would having 2 x values make it no longer a function?
• The definition of a function is as follows:
A function takes any input within its domain, and maps this to 1 output.
The domain of a function is what input values it can take on. For an example, the function f(x)=1/x cannot take on x values of x=0 because that would make the function undefined (1/0 = undefined).
The range is what possible y values a function can take on. Some functions, such as 'y=x' have a infinite range, meaning they can output any y value. Other functions, such as 'y=sin(x)' have a run from -1 to 1.

Function Notation
It is very important to understand the notation we use for functions.
An equation is simply two expressions set to one another, like y=2x.
But if we were drawing the graphs of some of our equations then, then we might get confused. If we had two equations y=2x and y=5x-3 how could we differentiate between the two; aka reference one easily?

Well if we define a function as an equation then we can reference the equation as the function name.
The function name can be anything, f, g, h, etc.
We would write that like so:
f(x) = 25x
So we write the function name followed by parenthesis, and inside the parenthesis we would write our (independent) variables to that function. We can actually have more than 1 variable, which you'll see in advanced courses like Multivariable Calculus.
f(x, y) = 25x + 50y

Now we can easily reference as a function by its name like g(x) or h(x) which helps us differentiate between all of our functions.

Hope this helps,
- Convenient Colleague
• f(-7) means: whats the y value when x is -7, right?
• That is correct.
(1 vote)
• Can someone explain what a discrete function is in really simple terms, like you’re explaining to a sixth grader?
• domain is x
(1 vote)
• Does anyone else listen to this in 1.75 speed, and still understand everything easily?
• I do and English is not even my native language
(1 vote)
• what about the numbers it does not have a dot for
• Well, I suppose you would find an equation (most likely equations, may find by math or graphing calculator), then you would solve for them.
You may use many methods for finding an equation for a scatter plot. You would find the best correlation and then find two points and use point-slope form and find the equations. But for scatter, plots that are supposed to function the x-values need to have different y-values to be considered a function.
And those are more advanced stuff you are asking about right now. Depending on what math level you are on, you either learned this before or are going to learn this in the future.
Tell me if this was confusing.