Expert: Sherman D. - 4/19/2006

Question
1)  Sketch and label appropriately the graph of a function f using the following properties:  f is decreasing on (- infinity, -1), increasing on )-1, infinity), has a y-intercept of 2, and a minimum y-value of -3.  (more than one correct graph is possible).

2)  Graph g(x)= -f(x-1)+2.

3)  Determine whether f(x)=3x^4-x^2 is even or odd.

4)  Let f(x)=x^2-3x and g(x)=2x-4, find and simplify each expression.

 a)  f(x)+g(x)

 b)  g o f

 c)  f(g(0))

Answer
For help on 1 and 2, i recommend asking for help at answers.yahoo.com

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3) Determine whether f(x) = 3x^4 - x^2 is even or odd.
3x^4 - x^2 = x^2(3x^2 - 1)

Its even.

for a graph, go to www.calculator.com/calcs/GCalc.html

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4) Let f(x)=x^2-3x and g(x)=2x-4, find and simplify each expression.

a)
f(x) + g(x)
(x^2 - 3x) + (2x - 4)
x^2 - 3x + 2x - 4
f(x) + g(x) = x^2 - x - 4

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b)
g o f = g(f(x))
g(x^2 - 3x) = 2(x^2 - 3x) - 4
g(x^2 - 3x) = 2x^2 - 6x - 4

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c)
f(g(0))
g(0) = 2(0) - 4 = 0 - 4 = -4
f(-4) = (-4)^2 - 3(-4)
f(-4) = 16 + 12
f(-4) = 28