Hi Rada! I will try to explain the strategy to solve this question. However, I can't tell exactly what concepts are confusing you, so feel free to ask additional questions if I didn't solve your problem.

In order to answer all parts of this question, you first need to figure out what function m is. The only way to do this is to look at the points you are given and make a guess that fits them. Here, I notice that the values for m(x) increase by one each time, so it looks to me like m is a linear function(*). Linear functions have the form ax+b, where a represents the slope and b represents the y-intercept. (Let me know if you would like further explanation on this.)

I notice that x increases by 2 each time m increases by one, so our function m has a slope (change in y / change in x) of 1/2. So, our equation so far is m(x) = (1/2)*x+b.

Now we only need to find b, the y-intercept. The simplest way to do this is to extend the table from the problem down to x=0. Each time x decreases by 2, m(x) will decrease by 1:

_______________

x : 0 : 2 : 4 : 6 : 8 : ...

_______________

m: -2: -1 : 0 : 1 : 2: ...

_______________

So, m's y-intercept is -2.

A more "mathematical" way to do this is by using a point on m to solve our equation, m(x) = (1/2)x+b. Let's try using the point x=8, m(x)=2:

2 = (1/2)*8 + b

2 = 4 + b

-2 = b

Either way, we get that b=-2. So the equation for m is (1/2)*x-2.

With this equation, we can answer part A directly by plugging these values in. For B, you will need to find the

y-intercept of h (which is h(0)). For C, drawing both functions on the same graph (or a graphing calculator like Desmos) should help you find the answer. Look for what part of the graph where m(x) is higher.

I hope this has been helpful! Again, please let me know if there's anything I can further clarify.

Elana

(* If we are being precise, there is more than one function which could fit the points you are given. However, the other functions which fit are not nice to work with, so we will just ignore them.)

Rada H.

Thank you so much, I get way better now03/14/20