Which statement correctly describes the monotonic behaviour of the two curves and ?

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Which statement correctly describes the monotonic behaviour of the two curves

y = 4^{x}

and

y = \bigl(\tfrac{1}{4}\bigr)^{x}

? (a)

y = 4^{x} \text{ is increasing for } x>0 \text{ and decreasing for } x<0, \text{ whereas } y = \bigl(\tfrac{1}{4}\bigr)^{x} \text{ is decreasing for } x>0 \text{ and increasing for } x<0

(b) Both curves are decreasing for all real

x

. (c)

y = 4^{x}

is increasing, whereas

y = \bigl(\tfrac{1}{4}\bigr)^{x}

is decreasing. (d) Both curves are increasing for all real

x