The function is related to by a reflection in the –axis

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The function

h(x)=-3^{x}

is related to

k(x)=3^{x}

by a reflection in the

x

–axis. Use this information to answer the following. (i) Determine the

y

–intercept of

h

. (ii) State the horizontal asymptote of

h

. (iii) For all real

x

, state whether

h(x)

is positive, negative or zero. Give a reason. (iv) Sketch the graph of

h

, clearly showing the intercept, the asymptote and the general shape. (v) Explain, with reference to your sketch, whether

h

is increasing or decreasing on its domain.