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Why is graph paper used when sketching?
to know exactly what point your going to draw on
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
Is fx a function if fx equals 0 if x is a rational number and 1 if x is an irrational number?
Yes. It is a piece-wise function with the limit: lim{x->0}= 0 You graph both parts as two series of dotted lines since there are infinite rational and irrational possibilities
How do you determine if the graph of a function is concave down without looking at the graph?
If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.
What is the graph of a linear function?
the graph is called a line
