Let . (i) Describe step by step how the graph of can be transformed to obtain the…
MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
Let f(x)=3x−2+1.
(i) Describe step by step how the graph of y=3x can be transformed to obtain the graph of y=f(x).
(ii) Sketch the graph of y=f(x) on the Cartesian plane, marking clearly:
(a) at least three distinct points that lie on the curve,
(b) all intercepts with the coordinate axes,
(c) the equation of its asymptote.
(iii) Find the inverse function f−1(x).
(iv) On the same set of axes, sketch the graph of y=f−1(x) and label the point where the two graphs intersect.