A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Let

f(x)=3+2\,\log_{5}(x-4)

. (i) Determine the domain of

f

. (ii) Determine the range of

f

. (iii) Find the

x

–intercept (if any) and comment on the presence of a

y

–intercept. (iv) Sketch the graph of

y=f(x)

, clearly indicating the vertical asymptote, the intercept(s) found in part (iii), and two additional convenient points.