girlmeetsvce
This is what each what each part is asking and how you should go about answering each:
a) Using the information given for the Gold taxi, formulate a function that corresponds to the cost (dollars) in terms of d (km).
b) Using the information given for the Purple taxi, formulate a function (G(d)) that corresponds to the cost (dollars) in terms of d km. Note that unlike the Gold taxi, the Purple taxi fee has two conditions and therefore the function P(d) will be a hybrid/piecewise function as you must define both conditions.
c) Graph both the functions, pretty self explanatory, with d km on the x-axis and cost on the y-axis. I'd recommend consulting your CAS for this (usually these types of questions are tech enabled).
d)
i) you need to set d=7 as an input for the function G(d). G(d) means 'the cost of the Gold Taxi (dollars) with respect to distance (km)', so given km you can find the cost.
ii) similar to part i), you need to use d=12 as an input for the function P(d). However, since there are two conditions, you need to ask: into which domain will d=12 fit into? In this case, d=12 fits into the domain of P(d)=25, and thus you'll use that function to find your answer.
e) There are two ways you can answer this question: inspecting the graph drawn in part c) or setting d=15 as an input for both function (remember for function P(d) you must assess which domain this input fits into).
f) Go back to the graph drawn in part c) and assess: where is the cost ($) for the function P(d) lower than that of G(d). From what I can see by graphing this on my CAS is that the cost of the purple taxi is lower than that of the Gold taxi after the intersection point of the two graphs. Therefore, we can state the distances for which the Purple taxi is the cheaper option with a domain: d∈ (6,∞) or for d>6, where the value of d at the intersection point is the first value in the domain. This value however, is given a not inclusive sign as it is the point where the cost of the Gold and Purple taxi are the same, not where the purple taxi is cheaper.
