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Course: Algebra 1 > Unit 8
Lesson 1: Evaluating functions- What is a function?
- Worked example: Evaluating functions from equation
- Evaluate functions
- Worked example: Evaluating functions from graph
- Evaluating discrete functions
- Evaluate functions from their graph
- Worked example: evaluating expressions with function notation
- Evaluate function expressions
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Evaluating discrete functions
Given the graph of a discrete function, Sal shows how to evaluate the function for a few different values.
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What makes this function discrete? Why have it in the title but not address it in the video? Just curious.(38 votes)
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.(42 votes)
Which function passes through the points (2, 3) and (4, 4)(6 votes)- 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.(6 votes)
whats a way we would use discrete function in real life.(4 votes)
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.(8 votes)
- 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?(2 votes)
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(8 votes)
- f(-7) means: whats the y value when x is -7, right?(4 votes)
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?(5 votes)
- Does anyone else listen to this in 1.75 speed, and still understand everything easily?(4 votes)
- I do and English is not even my native language(1 vote)
- what about the numbers it does not have a dot for(2 votes)
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.(3 votes)
- what if two different inputs have the same ouput. Is that a function?(2 votes)
- That is okay, think of the quadratic parent function y=x^2, you have (-1,1)(0,0)(1,1), which is a function. So yes it is fine.(3 votes)
- what is a discrete function(3 votes)
- A discrete function is a function with distinct and separate values. This means that the values of the functions are not connected with each other.(1 vote)
Video transcript
- [Instructor] What we have
here is a visual depiction of a function. And this is a depiction
of Y is equal to H of X. Now when a lot of people see
function notation like this they see it as somewhat
intimidating until you realize what it's saying. All a function is, is
something that takes an input, in this case it's taking X as
an input and then the function does something to it and then
it spits out some other value which is going to be equal to Y. So for example what is H
of four based on this graph that you see right over here? Pause this video and think through that. Well all H of four means
is when I input four into my function H what
Y am I spitting out? Or another way to think about
it, when X is equal to four, what is Y equal to? Well when X is equal to four,
my function spits out that Y is equal to three. We know that from this
point right over here, so Y is equal to three, so H
of four is equal to three. Let's do another example. What is H of zero? Pause the video try to work that through. Well all this is saying is
if I input an X equals zero into the function what is going
to be the corresponding Y? Well when X equals zero we
see that Y is equal to four. So it's as simple as that. Given the input what is
going to be the output? And that's what these points
represent, each of these points represent a different
output for a given input. Now it's always good to keep
in mind one of the things that makes it a function is
that for given X that you input you only get one Y. For example if we had two dots
here, then all of a sudden or we have two dots for X
equals six, now all of a sudden we have a problem
figuring out what H of six would be equal to because
it could be equal to one or it could be equal to three. So if we had this extra dot
here, then this would no longer be a function. In order for it to be a
function for any given X, it has to output a unique
value, it can't output two possible values. Now the other way is possible. It is possible to have two
different X's that output the same value. For example, if this was circled
in what would H of negative four be? Well H of negative four when
X is equal to negative four, you put that into our function
it looks like the function would output two. So H of negative four
would be equal to two. But H of two is also equal
to we see very clearly there, when we input a two into the
function, the corresponding Y value is two as well. So it's okay for two
different X values to map to the same Y value that works. But if you had some type of
an arrangement, some type of a relationship where
for a given X value you had two different Y values,
then that would no longer be a function. But the example they gave
us is a function assuming I don't modify it.