2.3 Graphs of functions and sketchingIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is the graph of a function f?
What is the difference between 'draw' and 'sketch'?
What must be labelled on a sketch?
How do you find a zero of f with your GDC?
How do you graph the difference of two functions?
What is a window on a GDC?
How do you transfer a graph from the GDC screen to paper?
How do you show an asymptote on a sketch?
Where do two graphs meet?
Zeros and vertex of x^2-4x-5?
What shape is the graph of 20+70\times0.9^t?
How accurate should GDC answers be?

Exam questions on 2.3 Graphs of functions and sketching

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).