SOLUTION: Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|. Also use the graph to solve the inequality f(x

Question 992558: Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|. Also use the graph to solve the inequality f(x)<0.
f(x)=9+3x-2x^2
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|.
Also use the graph to solve the inequality f(x)<0.
f(x)=9+3x-2x^2
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The domain of the function f is the entire number line, i.e. the set of all real numbers. (It is so for any polynomial).

The domain of the function g is the same entire number line, i.e. the set of all real numbers.
The plots of f and g are shown in the Figure below. The plot of g is in green. Partly it is over-posed the plot of f.

The roots of f are 3 and .
f(x) < 0 in two semi-infinite intervals (, ) and (3, ).

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