Jack of All Trades

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MA240 College Algebra
Assignment 6

1.Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y.

x|y| = x + 9
|y|=(x+9)/x
(A fixed value of x y can take 2 values then the equation does not define a function with x as independent variable.)

2.Use the graph of the function to estimate:

a.f(2)

b.f(–4)

c.All x such that f(x) = 0

a. f(2)=6 due to the fact that (2,6) is in the line

b. f(-4)=0 due to the fact that (-4,0) is in the line

c. x - -4 because from #b f(-4)=0

3.For the following graph:

a.Find the domain of f.

b.Find the range of f.

c.Find the x-intercepts.

d.Find the y-intercept.

e.Find the intervals over which f is increasing.

f.Find the intervals over which f is decreasing.

g.Find the intervals over which f is constant.

h.Find any points of discontinuity.

a. F(x) is a parabola so f(x) = ax2+bx+c and the domain of all polynomials are real numbers because f(x) can be computed for every x real. The domain is R.

b. Vertex is (1,4) and f has a maximum there, then f(x)< for every x real and for every y< we can find x/f(x) = y. The range is -00,4)

c. The x-intercepts of the graph are (-1,0) and (3,0).

d. The y intercept of the graph is (0,3)

e. f is increasing from -00 to the x-coord of the vertex to +00 so f is increasing in (-00,4)

f. f is decreasing from the x-coord of the...
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