Consider the function

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

Problem

2. Consider the function

y=\left(\dfrac12\right)^{x-3}

. Answer the following: (a) Find the domain and range. (b) Write the equation of the horizontal asymptote. (c) Determine the coordinates of the

y

-intercept. (d) Prepare a table of values for

x=0,1,2,3,4,5

and the corresponding

y

values correct to two decimal places. (e) Using the results above, sketch the graph on a suitable scale. Clearly label the asymptote,

y

-intercept, and indicate whether the curve represents exponential growth or decay.