Question

I dont understand this at all

Compare and contrast these four functions using complete sentences. Focus on the slope and y-intercept first, and then on any additional properties of each function

Answer 1

Basically, f(x), g(x), h(x), j(x) are functions.

Answer 2

A function takes inputs and produces an output.

Answer 3

yes i understand that

Answer 4

So, f(x) describes a function called f that takes an x value, and outputs a y value.

There are many different valid ways ways to represent this relationship of x and y.

Answer 5

One way is through words

Answer 6

see i dont understand how to classify them from biggest to smallest y intercepts

Answer 7

Ok, you have to translate the sentence into an equation. We're describing how much money Jesse has. We'll start off with the first part: "Jesse got $5 from his dad," so the amount Jesse has is: y= 5

Answer 8

okay

Answer 9

The next part is, "he makes $2 each time he walks the neighbors dog" We'll represent each time he walks the dog as x, so the the amount of money he gets from walking the dog is: 2x

Answer 10

Combine this with the money he got from his dad, and we get: y=5+2x

Answer 11

The y-intercept is the y value, when x is 0

Answer 12

So for the first one, we have a y-intercept of: y=5+2(0)=5

Answer 13

so basically y=5 for the first one?

Answer 14

Yeah

Answer 15

okay i get that part

Answer 16

So for g(x)...

Answer 17

You're 3 points that are on a line

Answer 18

yes

Answer 19

So, you can find the equation of the line using any 2 points that lie on the line

Answer 20

y = mx + b

Answer 21

m is the slope

Answer 22

You can find the slope using this formula: \[slope=\frac{y_2-y_1}{x_2-x_1}\]

Answer 23

Once you find the slope, you can find the value of b by plugging in m, and an (x,y) value

Answer 24

b is your y intercept

Answer 25

For h(x), you can just look at the graph for the y-intercept, which is 5

Answer 26

For j(x), plug in x = 0, to get the y-intercept, which is: -5

Answer 27

@uhhhhhh im not getting the g(x) part

Answer 28

Ok, basically, we're trying to find the equation of the line, which is in the form y = m*x + b. The constants m and b characterize the line.

Answer 29

The m value is the slope of the line. You can find it by using this formula:\[m=slope=\frac{y_2-y_1}{x_2-x_1}\]..........................................................................
The \[x_2,x_1,y_2,y_1\] are coordinates of two points on the line:\[(x_1,y_1)\ and\ (x_2,y_2)\]

Answer 30

For example: I could choose (-2,-1) and (2,-9)

Answer 31

You should get an m value of: -2

Answer 32

yeah i get that

Answer 33

So now you have: y = -2x + b

Answer 34

Plug in a set of coordinates to find b. For example: (-2,-1)

Answer 35

(-1) = -2(-2)+b

Answer 36

b is your y-intercept

Answer 37

b is -5

Answer 38

okay i get that

Answer 39

Summary: a straight line is defined by two things: how steep the slope is, and where the line hits the y-axis. In terms of algebra, in the line equation
y = m*x + b
m measures how steep the line is, and b measures where the line hits the y-axis