By the end of this section you should be able to:
Section 1: Real functions
understand the definition of a real function;
use the notation for intervals of the real line;
recognise and use the graphs of the basic functions described in the audio section;
understand the effect on a graph of translations, scalings, rotations and reflections;
understand how the shape of a graph of a function features properties of the function such as increasing, decreasing, even and odd.
Section 2: Graph sketching
determine the x-intercepts and y-intercept of a given function f;
determine the intervals on which a given function f is positive or negative;
determine the intervals on which a given function f is increasing or decreasing, and any points at which f has a local maximum or local minimum;
describe the asymptotic behaviour (if any) of a given function f;
sketch the graph of a given function.
Section 3: New graphs from old
sketch the graph of a combination of two functions, one of which is a trigonometric function;
sketch the graph of a hybrid function, whose rule is defined by different formulas on different parts of its domain.
Section 4: Hyperbolic functions
define the hyperbolic functions cosh x, sinh x and tanh x, and be familiar with their properties;
sketch the graphs of cosh x, sinh x and tanh x, and their reciprocals.
Section 5: Curves from parameters
plot a curve that is specified by a parametric representation;
obtain the equation of a curve that is specified by a parametric representation, in simple cases;
sketch a conic whose equation is given in standard form.
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