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
(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:
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...