2.3 Graphs of functions and sketchingIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.3 Graphs of functions and sketching

1. A student uses a GDC to graph $f(x)=x^2-4x-5$ and then transfers the graph to paper.
   Find the coordinates of the $y$-intercept and of the vertex of the graph of $f$. These are the points to label on a sketch.2 marks
2. A small factory makes $x$ hundred items per week, where $0\le x\le15$. The weekly revenue is $R(x)=30x$ and the weekly cost is $C(x)=2x^2+50$, both in thousands of AED. The weekly profit is $P(x)=R(x)-C(x)$.
   Use your GDC to find the values of $x$ for which the factory breaks even, that is $P(x)=0$.2 marks
3. A cup of tea cools in a room. Its temperature, $T$ °C, at $t$ minutes after it is poured is modelled by $T(t)=20+70\times0.9^t$, for $0\le t\le30$.
   Use your GDC where appropriate. (i) Write down $T(0)$. (ii) Find the temperature of the tea after 10 minutes. (iii) Find the time at which the temperature of the tea is 50 °C.3 marks