MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions
Problem
Four standard real functions are given below.
F1: y=∣x∣F2: y=x1 (x=0) F3: y=x2F4: y=x
Four sets of graph properties are described.
P1: Passes through the origin and has constant slope 1 at every point.
P2: V-shaped curve with vertex at the origin and opening upwards.
P3: Hyperbola with both the x-axis and y-axis as asymptotes.
P4: Parabola opening upwards with vertex at the origin.
(i) Match each property set P1–P4 with the corresponding function F1–F4, giving one reason for every match.
(ii) For the function matched to P3, state its domain, range and write the equations of its asymptotes.
(iii) For the function matched to P2, calculate its value at x=−5 and at x=3.