Consider the linear function and the quadratic function .
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Consider the linear function f(x)=2x−3 and the quadratic function g(x)=x2.
(i) Plot both functions on the same set of Cartesian axes for −3≤x≤3. Label clearly all intercepts with the axes.
(ii) Using your sketches, describe the nature of each graph with respect to:
(a) straightness or curvature,
(b) symmetry,
(c) turning point(s).
(iii) Explain, without using calculus, why the rate of change of g(x) cannot remain constant for all x, whereas that of f(x) does.