How can we apply this information in real life? I mean, where do we see these types of graphs in our day-to-day lives? I don't get how this would be useful.

We Don't Learn Only Things That We can use in life but we also learn things to enrich our minds so that we can stretch them and learn how to problem solve and become independent instead of dependent! Do You know what I Mean?

is there a reason that sal always uses the x as the input and receives a y value in return and not the other way around

Tradition and the Cartesian Plane which uses x as the input and y as the output

Around 1:16 wouldn't it be -14+-5=-9 instead of -14+-5=-19?

Same signs add numbers and keep sign, so since both are negative, add numbers (14+5) and keep the negative sign to get -19.

I don't know where is the best place to ask this question , and I am sorry for any bad English. Can i have a function inside it self, is there a way to solve this or am I making this up ? for example f(x)=f(x)+2+x; if I replace it with f(2) would there be a way to solve this ?

Your example doesn't really involve a function. Notice that we can subtract f(x) from both sides to get 0=2+x. Now subtract 2 from both sides to get x= -2. So we just have an equation of one variable that we can solve. What we _can_ do is define functions recursively. For example, we can define a function over the whole numbers: f(0)=1 f(n)=n*f(n-1) So if we want to find f(3), this is 3•f(2)=3•(2•f(1))=3•2•(1•f(0))=3•2•1•1=6. If you meant something else, comment back.

idk how to do this fr 💀

What is happening here is basically you substituting the variable function [ex: f(x)] with the graphs. For the example -2⋅f(-6)+g(1), you find where -6 and 1 are on the graphs, since those are the x values, then substitute the values in the equation. Since g(1) lines up with -5, that is the value. After you substitute in the values just solve as a normal equation and you have the answer. Hope this cleared things up.

how old do you have to be to do this stuff?

There's no age limit! However, I think most schools teach this in grades 8-9.

Main content

Algebra 1

Course: Algebra 1 > Unit 8

Lesson 1: Evaluating functions

Worked example: evaluating expressions with function notation

Name: Worked example: evaluating expressions with function notation
Uploaded: 2013-06-06T21:47:23Z
Description: Evaluating -2⋅f(-6)+g(1) given the graphs of f and g.

Google Classroom

Evaluating -2⋅f(-6)+g(1) given the graphs of f and g. Created by Sal Khan.

Want to join the conversation?

Sort by:

c8kboy
Posted 4 years ago. Direct link to c8kboy's post “How can we apply this inf...”
How can we apply this information in real life? I mean, where do we see these types of graphs in our day-to-day lives?

I don't get how this would be useful.
Button navigates to signup pageComment on c8kboy's post “How can we apply this inf...”
(36 votes)
Answer
- KDP28
  Posted 3 years ago. Direct link to KDP28's post “We Don't Learn Only Thing...”
  We Don't Learn Only Things That We can use in life but we also learn things to enrich our minds so that we can stretch them and learn how to problem solve and become independent instead of dependent! Do You know what I Mean?
  Button navigates to signup page
  (9 votes)
yig646
Posted 6 years ago. Direct link to yig646's post “is there a reason that sa...”
is there a reason that sal always uses the x as the input and receives a y value in return and not the other way around
Button navigates to signup pageButton navigates to signup page
(9 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Tradition and the Cartesi...”
  Tradition and the Cartesian Plane which uses x as the input and y as the output
  Comment on David Severin's post “Tradition and the Cartesi...”
  (16 votes)
Gilbert
Posted 4 years ago. Direct link to Gilbert's post “Around 1:16 wouldn't it b...”
Around
1:16
wouldn't it be -14+-5=-9 instead of -14+-5=-19?
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “Same signs add numbers an...”
  Same signs add numbers and keep sign, so since both are negative, add numbers (14+5) and keep the negative sign to get -19.
  Button navigates to signup page
  (6 votes)
Abdo Reda
Posted 6 years ago. Direct link to Abdo Reda's post “I don't know where is the...”
I don't know where is the best place to ask this question , and I am sorry for any bad English.

Can i have a function inside it self, is there a way to solve this or am I making this up ?
for example f(x)=f(x)+2+x; if I replace it with f(2) would there be a way to solve this ?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- kubleeka
  Posted 6 years ago. Direct link to kubleeka's post “Your example doesn't real...”
  Your example doesn't really involve a function. Notice that we can subtract f(x) from both sides to get 0=2+x.
  
  Now subtract 2 from both sides to get x= -2. So we just have an equation of one variable that we can solve.
  
  What we can do is define functions recursively. For example, we can define a function over the whole numbers:
  f(0)=1
  f(n)=n*f(n-1)
  
  So if we want to find f(3), this is 3•f(2)=3•(2•f(1))=3•2•(1•f(0))=3•2•1•1=6.
  
  If you meant something else, comment back.
  Comment on kubleeka's post “Your example doesn't real...”
  (14 votes)
Caroline
Posted 4 years ago. Direct link to Caroline's post “how old do you have to be...”
how old do you have to be to do this stuff?
Button navigates to signup pageComment on Caroline's post “how old do you have to be...”
(0 votes)
Answer
- flowerfarmer9
  Posted 4 years ago. Direct link to flowerfarmer9's post “There's no age limit! How...”
  There's no age limit! However, I think most schools teach this in grades 8-9.
  Button navigates to signup page
  (11 votes)
Hadi
Posted 5 months ago. Direct link to Hadi's post “The questions in the vide...”
The questions in the video are so easy. Can they be harder?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
Susan Ortega
Posted 7 years ago. Direct link to Susan Ortega's post “How do you find the domai...”
How do you find the domain and range of the following question: Sal is driving 70mph. What is a reasonable domain and range if the total distance from Houston to Miami is 980 miles.
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
gasca
Posted 3 months ago. Direct link to gasca's post “idk how to do this fr 💀”
idk how to do this fr 💀
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- 123473
  Posted a month ago. Direct link to 123473's post “What is happening here is...”
  What is happening here is basically you substituting the variable function [ex: f(x)] with the graphs. For the example -2⋅f(-6)+g(1), you find where -6 and 1 are on the graphs, since those are the x values, then substitute the values in the equation. Since g(1) lines up with -5, that is the value. After you substitute in the values just solve as a normal equation and you have the answer. Hope this cleared things up.
  Button navigates to signup page
  (2 votes)
donovan.vanness
Posted 2 years ago. Direct link to donovan.vanness's post “Why can I never remember ...”
Why can I never remember this?
Button navigates to signup pageComment on donovan.vanness's post “Why can I never remember ...”
(2 votes)
Answer
Avani Mohindra
Posted 4 years ago. Direct link to Avani Mohindra's post “at 1:06, why does Sal say...”
at
1:06
, why does Sal say g of 1 = -5, when there is also 7? Which one is it? Thanks
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “No, there isn't also a 7....”
  No, there isn't also a 7.
  g(1) means you need to find the output value of g(x) when x=1. g(x) is the red dashed line. When x=1, the y=value that is on the red dashed line is -5.
  
  I don't see where you get the 7. The other line is f(x) and f(1)=8, not 7.
  Button navigates to signup page
  (1 vote)

Video transcript

We're asked to evaluate negative 2 times f of negative 6 plus g of 1. And they've defined, at least graphically, f of x and g of x here below. So let's see how we can evaluate this. Well, to do this, we first have to figure out what f of negative 6 is. So our input into our function is negative 6. And we'll assume that's along the horizontal axis. So our input is negative 6. And based on our function definition, f of negative 6 is 7. So this thing. Let me write this down. f of negative 6 is equal to 7. And what is g of 1? Well, once again, here's our input axis. And then the function says that g of 1, which is right over there, is negative 5. g of 1 is equal to negative 5. So this statement simplifies to negative 2 times f of negative 6, which is 7. So times 7 plus g of 1, which is negative 5. So plus negative 5, which simplifies to-- let's see. Negative 2 times 7 is negative 14 plus negative 5, which is negative 19. And we are done.