Rational functions

9000009907

Level: 
C
Consider a function \[ f(x) = \frac{k} {x} \] with a nonzero real parameter \(k\). Suppose that the value of the coefficient \(k\) changes, but the sign of \(k\) remains the same. Describe which of the properties of \(f\) is changed.
None of the above, both functions have the same parity, monotonicity and range.
The function changes its parity (from an odd function into an even function or from en even function into an odd function).
The range of the function changes.
The function changes the type of monotonicity on the sets \(\mathbb{R}^{+}\) and \(\mathbb{R}^{-}\) (either from an increasing function into a decreasing function or vice versa).

9000007709

Level: 
B
Identify a correct statement which concerns the function \(f(x) = -\frac{5} {x} - 3\).
None of the statements above is true.
The function \(f\) is bounded above.
The function \(f\) is an even function.
The function \(f\) is a decreasing function on \((0;\infty )\).
The function \(f\) is an odd function.

9000007707

Level: 
B
Identify a correct statement which concerns the function \(f(x) = 2 -\frac{1} {x}\).
None of the statements above is true.
The function \(f\) is bounded above.
The function \(f\) is an even function.
The function \(f\) is a bounded function.
The function \(f\) is an odd function.