Help por favor! Algebra 2!!

Question

anonymous · Answer

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

hero · Answer

Well, at first glance, we can see that the diagram presents the four different ways to express a function:

1. Verbally
2. Numerically
3. Graphically
4. Algebraically

hero · Answer

The next thing to observe would be to notice that each are linear functions.

hero · Answer

From there, you can began to point out more specific things like slope and y-intercept. And whether the functions are increasing or decreasing.

anonymous · Answer

How do you do that?

hero · Answer

If you were asked to come up with a linear expression for f(x), do you think you could do it?

anonymous · Answer

Nope. Idk what a linear expression is.

hero · Answer

A linear expression is the part of a linear function that includes the slope and the y-intercept. 

For example, the linear function f(x) = `mx + b` has slope, m, and y-intercept, b. 

The mx + b is the linear expression.

hero · Answer

For example if you had 

f(x) = 7x + 3, then 7 = m, and b = 3 are the slope and y-intercept respectively.

anonymous · Answer

Oh okay

hero · Answer

All you have to do is convert each of your given functions to algebraic form, then explain how you did it. You know that if the slope is positive, then it is increasing. If the slope is negative, then it is decreasing.

hero · Answer

Also, for the table, to find the slope you need to use the slope formula and the slope-intercept formulas to write its algebraic form:

Slope Formula
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$$$y = mx + b$$

hero · Answer

Just remember that for the table function $y = h(x)$

anonymous · Answer

Thank you :)

ness9630 · Answer

Didn't Hero already help?

hero · Answer

@ExtremeAnon, were you able to come up with the expression for the first function?

anonymous · Answer

Hi sorry my computer froze & I was eating dinner. 
No, I wasn't able to. I'm still confused. It's just no clicking in my head :P

anonymous · Answer

@Hero

hero · Answer

Initially, Jessie got $5 from his dad, then each time he walks his dog, he gets $2. For this, you start by making a table: x = how many times he walks the dog y = how much he got paid in total x|y 0|5 1|7 <1st time he walks the dog> 2|9 <2nd times he walks the dog> 3|11 <3rd time he walks the dog>

anonymous · Answer

mhmm

hero · Answer

If you graph those points, it will be much clearer to see. The goal is to figure out the slope and y-intercept.

anonymous · Answer

i know how to figure those out
i'm just not sure what kind of answer my teacher is looking for

hero · Answer

You should include the following observations in your answer:

1. The different ways the functions are presented (verbally, numerically, graphically, algebraically)

2. Acknowledge that each are linear functions
3. Write each function in their algebraic forms and express explicitly what their slopes and y-intercepts mean. 

4. Observe whether or not the functions are increasing or decreasing. 

That should be enough. These are only linear functions, so there is not much more you can describe beyond that.

anonymous · Answer

Okay, thank you :)