Which of the reciprocal functions has a vertical asymptote at = 3 a) f(x) = 1 За+1 O b) f(x) = 1 3 x+1 Oo f(z) = 31 3x-1 O d) f( x 1 x+

For positive numbers a and b, the interval0 ≤ x ≤ 6 Find the maximum value of the function f(x) = x^a(6 − x)^b

Plot the graphs of the following functions on the specified interval:  a) f(x) = x2 + 3 x - 1 on [-4, 2] b) g(x) = 1 x2-4 on [-3, 3] ) f(x) = x + 1 x for [-10, 10].

Find f(x) and g(x) such that for f(g(x)) = h(x) for a) h(x) = square root of 3^x-87 b)h(x)= 2/ ln (x+5)  c) h(x)= (x-3)^5 + square root of x-3 2. Which of the following can be written as a power function? Justify your answers. a) 5/2x b) square root of x-4