Let and . Answer the following, keeping both graphs on the same pair of…
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Let f(x)=2x and g(x)=2x−3+1. Answer the following, keeping both graphs on the same pair of axes.
(i) Describe geometrically how the graph of g is obtained from the graph of f.
(ii) Sketch both graphs, labelling their y–intercepts and horizontal asymptotes.
(iii) Using your sketch, estimate the coordinate(s) of the point(s) where the two graphs intersect.
(iv) Verify your estimate algebraically by showing that the two functions intersect at the point found in part (iii).