Question

1.Give a quadratic function q(x) with a vertex of (-1, 2).

2. Give a function h(x) which does not have an inverse function.

3. Give a polynomial function g(x) with zeros 1,2,3

4. Give an exponential function s(x) passing through (0,2) and (4,1).

5. Give a rational function R(x) with a zero of 2 and a vertical asymptote of x=3.

Answer 1

q(x) = 73(x+1)^2+2
h(x) = x^2
g(x) = (x-1)(x-2)(x-3)

Since x^0=1 for any x, we have s(x) = 2*a^(kx) for some a and k.
2*1/2 = 1, so
s(x) = 2*4^(-x/2)

r(x) will involve something/(x-3)
x-2 is zero at x=2, so
r(x) = (x-2)/(x-3) will work