10G (3.1) Intro to Functions: The 5 things to know about them.

10G (3.1)
Introduction to Functions: Five things you should know

In the past chapters, we had something like this:
 

Now, we have something like this:
 

Multiple Choice

Which of the following is an equation?

• 10 + x

• x - 9 > 10

• 5 + 8

• 2 + 0 = 2

• $$\frac{7}{2x}$$

Multiple Choice

Which of the following is an equation?

• 10 + x = 17

• 3x > 10

• 5x + 2

• 2 + 6

• $$\frac{2x}{3}$$

Multiple Choice

Which of the following equations is a function?

[HINT: Which is an equation with two different variables in it?]

• 10 + x = 17

• 5x + 2 = 92

• 5x + 2 = 11

• 2x + 6y = 0

• $$\frac{2x}{3}-19\ =\ 8$$

Multiple Choice

Which of the following equations is a function?

[HINT: Which is an equation with two different variables in it?]

• y - x = 111

• 5x + 2 = 92

• 5x + 2 = 11

• 2x + 6x = 0

• $$\frac{2x}{3}-19\ =\ 8$$

Multiple Choice

Which of the following equations is a function?

[HINT: Which is an equation with two different variables in it?]

• 3x = 90

• $$x^{2\ }+6x\ =\ 0$$

• 5x + 2 = 11y

• 2x - x = 5

• $$\frac{2x}{3}-19\ =\ \frac{8}{x}$$

Multiple Choice

Which of the following equations is a function?

[HINT: Which is an equation with two different variables in it?]

• 6y = 42

• $$x^{2\ }+6x\ =\ 0$$

• 5y² + 2 = 11y

• $$6x^{5\ }+3x^2=\ 7$$

• $$y=\frac{2x}{3}-19\$$

Multiple Choice

What is the first thing you should know about Functions in math?

• They are equations with two different variables.

• They are things that work

• They are funcy equations

• They are equations with a variable that you can find

• They are features of something

The SECOND thing you should know about Functions (in math) is:

When you plug in a value for one of the variables and solve, you get the value of the other variable

Multiple Choice

FINISH THE FOLLOWING SENTENCE:

"When you plug in the value of one variable into a function and solve....

[HINT: What is the SECOND thing you should know about functions? ]

• ...you get the value of the other variable"

• ...something amazing happens"

• ...the problem gets really hard"

• ...you get an irrational number"

The THIRD thing you should know about Functions is that:

1. The variable that you plug in is called the Independent Variable(IV) (usually x ),

2. The variable you get from the function after plugging in is the Dependent Variable(DV) (usually y )

3. We say "y is a function of x" because the value of y depends on the value of x

4. Variables could be any letters but I'm going to use x for IV and y for DV to make it easier to talk about these things. They like mixing things up on the regents

WHY? So that we can write:
f(1) = 1 + 1 = 2
f(2) = 2 + 1 = 3
f(3) = 4
f(4) = 5
It's a short way of writing "this went in and that came out"
It could be h(x) or any letter, as long as you're consistent

Multiple Choice

The independent variable is:

• 1. The variable that you plug into the function

• The variable that does things on it's own.

• The variable that doesn't have any parent variables

• The variable that is not Democratic or Republican

• 1. The variable you get from the function after plugging in a value

Multiple Choice

The Dependent variable is:

• 1. The variable that you plug into the function

• The variable that does things on it's own.

• The variable that doesn't have any parent variables

• The variable that is not Democratic or Republican

• 1. The variable you get from the function after plugging in a variable

Multiple Choice

What is the FOURTH thing to know about Functions?

• That we can write $$f\left(x\right)$$  

  instead of writing $$y$$  

• That we can plug in values of variables

• That no two functions are alike

• That we can write functions using $$x$$ and $$y$$

The FIFTH thing to know about Functions is that you MUST get the same value for f(x) every time you plug in the same value for x into a function.

​It's not easy to think of what this looks like as an equation, but it's easy to see it in a chart

​x	​f(x)
​1	​1
​1	​2
1​	​3
1​	​4
1	​5

​f(x) is NOT a function of x

​We're going to talk about this more next time

1. Functions are equations with two different variables.

2. When you plug in a value for one of the variables and solve, you get the value of the other variable

3. When you plug in the Independent Variable [x] into a function, the Dependent Variable [y] comes out of the function

4. We can write that a variable [y] is a function of x by writing f(x)

5. If x stays the same, then f(x) must stay the same. Otherwise f(x) is not a function of x

​The 5 things to know about Functions