Math 0020 - Final Review Questions
1. Find the domain and range of the following:
(a) f(x) = xโ4
x2โ4(domain only)
(b) g(x) = โ2x+ 7
(c) h(x) = 3
โx+ 2
2. Sketch a graph of the following:
(a) g(x) = x2+ 6x+ 8 (also find the vertex and x-intercepts)
(b) i(x) = log2(x+ 1) โ2
(c) j(x) = 3โx+1 โ2
3. Among all the pairs of numbers (x, y) such that 2x+y= 20, find the pair for which the sum of the squares
is minimum.
4. Sketch a graph of the following:
(a) a(x) = โ1
x2+ 1
(b) b(x) = 2|x+ 2| โ 1
(c) c(x) = ๎โx2โ1,xโค1;
x2+ 1,x>1.
5. Suppose yvaries inversely as the cube of x, and that y= 0.005 when x= 10. What is ywhen x= 5?
6. If f(x) = x2โ1 and g(x) = 12
x+1 .
(a) Find f(3) and g(3).
(b) Find (f+g)(3) and (fโg)(3).
(c) Find (fโg)(x) and (fโg)(x).
(d) Find (gโฆf)(2).
(e) Find (gโฆf)(x).
7. Find the inverse of the following functions.
(a) f(x) = xโ1
3x+2
(b) g(x) = 3โx5
โ9
8. Find the vertex form, the factored form, the axis of symmetry, and the vertex of f(x) = x2+ 5x+ 6
9. Solve x2โ7x+ 10 = 0 by factoring *AND* by the quadratic equation.
10. Solve 10x+1 = 32xโ1.
11. Solve (4
9)2x+1 = (3
2)3xโ1
12. A population of 400 bacteria doubles every 3 hours .
(a) How many bacteria are there after 6 hours?
(b) Find asuch that P(t) = P0atmodels this population.
(c) Use this equation to find how many there are after 5.5 hours.
(d) Find ksuch that P(t) = P0ekt models this population.
(e) Use this equation to find how many there are after 2.5 hours.
13. Expand log( 5
q10x2
y3) completely.
14. Solve ln(x+ 1) + ln(x+ 4) = ln(x+ 2) + ln(x+ 5) for x.
