Answer:
(1) B. f(x)->0 as x->∞, f(x)->∞ as x->-∞
(2) D. [tex]f(x)= 2^{-x}+5[/tex]
Step-by-step explanation:
[tex]f(x) = b^x[/tex]. Given 0<b<1
'b' is between 0 and 1 so b should be a fraction
'b' is a fraction, so for positive value of x , the value of f(x) cannot be negative.
the graph of f(x) will goes close to 0 but it never cross x axis
So end behavior is f(x)->0 as x->∞
for negative values of x , the y value increases
So end behavior is f(x)->∞ as x->-∞
(2) f(x) = 2^x
When graph reflects across y axis, x becomes -x
so [tex]f(x)= 2^{-x}[/tex]
For translating up by 5 units we add 5 at the end
so [tex]f(x)= 2^{-x}+5[/tex]
