An exponential curve passes through the points and

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

3. An exponential curve passes through the points

A(0,1)

and

B(2,9)

. (a) Show that its equation can be written in the form

y=a^{x}

and determine the value of

a

. (b) Verify that both

A

and

B

satisfy the equation obtained in part (a). (c) Find the value of

y

when

x=-2

. (d) State the horizontal asymptote, domain, range, and describe the end behaviour of the curve as

x\to\infty

and

x\to-\infty

. (e) Draw a neat, labelled sketch of the graph, marking the points

A

B

, and the point found in part (c).