Consider the function .

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

Problem

Consider the function

f(x)= -2^{\,x}+3

. (i) State the domain of

f

. (ii) Explain, with reasons based on the transformations involved, the range of

f

. (iii) Describe in words the sequence of transformations applied to the graph of

y=2^{x}

to obtain the graph of

y=f(x)