Question

How to make a piece-wise function?

Answer 1

i'm having trouble with number 5

Answer 2

C = 14 ZAR for M <= 100 grams
C = 28 ZAR for 100 < M <= 200 grams
C = 35 ZAR for 200 < M <= 1000 grams

But put it in the proper form.

Answer 3

\[
C =
\begin{cases}
14 \text{ ZAR}, & \text{if }~ M \le \text{ 100 grams} \\
28\text{ ZAR}, & \text{if }~ 100 \lt M \le \text{ 200 grams} \\
35\text{ ZAR}, & \text{if }~ 200 \lt M \le \text{ 1000 grams} \\
\end{cases}
\]

Answer 4

ok! i wasnt sure how to do the second and third ones. How can we find the domain and range now?

Answer 5

Here C is along the y-axis and M is along the x-axis.
When they ask for domain, they are asking what are the permitted values for M?
M is the weight of the package in grams. In the problem the maximum allowed weight is 1000 grams because they say "no more than 1000 g". The minimum value of the package is zero although there is nothing to ship if the weight is actually zero. So we will exclude 0. The domain written as an inequality is: \(0 \lt M \le 1000\).
In interval notation, M is: (0, 1000]
(the left end of 0 is not included as indicated by "(" and the right end of 1000 is included as indicated by "]" ).

Answer 6

so how would you find y? y would be the cost to ship the package right?

Answer 7

In set notation, \[\left \{ M \in R | ~~ 0 \lt M \le 1000\right \}\]

Answer 8

would it just be {14,28,35} because it is only those values not a list?

Answer 9

Yes. For c) the range is {14, 28, 35}.

My previous reply is for part b) because they want the domain in set notation too.

Answer 10

my teacher doesn't like to use set notation so i don't have to do that part but thanks :)

Answer 11

Alright.

Answer 12

when i graph, how will i show my domain since its so large? i only have the 3 numbers for y but 1,000 numbers for x....

Answer 13

It is done by choosing the proper scales for the x and y axes.
x goes from 0 to 1000. We can choose 1 unit along the x-axis represents 100 grams and so 10 units will accommodate 1000 grams. Or we can choose 1 unit along the x-axis represents 200 grams and so 5 units will accommodate 1000 grams.

For the y-axis the values are 14, 28 and 35 ZAR (all multiples of 7). We can choose each division along the y-axis to represent 7 ZAR.

Answer 14

alright, i think ive got it :)

Answer 15

to find part E, you we find the inverse of the given function?

Answer 16

No, not the inverse.

The function's domain has three parts. Which domain is applicable when M = 283 grams?

Answer 17

The three domains are:
M <= 100
100 < M <= 200
200 < M <= 1000

which one applies to M = 283 grams?

Answer 18

the last one... but thats in rand ... shes trying to find how many euros the 35 ZAR is

Answer 19

@aum

Answer 20

Yes convert 35 ZAR to Euros. You can use Google to convert currencies:

https://www.google.com/search?biw=1280&bih=872&noj=1&sclient=psy-ab&q=35+ZAR+in+Euros&oq=35+ZAR+in+Euros&gs_l=serp.3...92956909.92961808.1.92962062.15.15.0.0.0.0.269.1497.8j5j1.14.0....0...1c.1.53.serp..6.9.1058.ft6q7KHGMss

Answer 21

It uses today's currency exchange rate of 1 ZAR = 0.071 Euro.

Answer 22

It uses today's currency exchange rate of 1 ZAR = 0.071 Euro.

But round the answer to 2 decimal places. 35 ZARs = 2.47 Euros.