9000007607 Level: BFind the range of the function \(f(x) = 2 - \frac{3} {x-2}\).\(\mathbb{R}\setminus \{2\}\)\(\mathbb{R}\setminus \{ - 2\}\)\(\mathbb{R}\setminus \{ - 2;3\}\)\((0;\infty )\)\(\mathbb{R}\)
9000007702 Level: BIdentify a correct statement which concerns the function \(f(x) = \frac{1} {-x+2}\).None of the statements above is true.The function \(f\) is an increasing function.The function \(f\) is bounded below.The function \(f\) has a maximum at \(x = 2\).The function \(f\) is decreasing on \((2;\infty )\).
9000007707 Level: BIdentify 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.
9000007709 Level: BIdentify 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.
9000014201 Level: BFind intersection points of the graph of the rational function \( f(x) = \frac{2x - 3} {x - 2} \) with \(y\)-axis.\(Y = \left [0; \frac{3} {2}\right ]\)\(Y = \left [\frac{3} {2};0\right ]\)\(Y _{1} = \left [0; \frac{3} {2}\right ]\text{ and }Y _{2} = \left [\frac{3} {2};0\right ]\)\(Y = \left [2;2\right ]\)
9000014202 Level: BFind the intersections of the graph of the rational function \(f(x) = \frac{x+2} {2-x}\) with \(x\)-axis.\(X = \left [-2;0\right ]\)\(X = \left [0;-2\right ]\)\(X_{1} = \left [0;-2\right ]\text{ and }X_{2} = \left [-2;0\right ]\)\(X = \left [2;0\right ]\)
9000014203 Level: BWhich of the statements from the following list is true for the function \(f(x) = -\frac{2} {x} + 1\)?The function \(f\) is a one-to-one function.The function \(f\) is an odd function.The function \(f\) is an increasing function.The graph of the function \(f\) is a hyperbola with branches in the second and fourth quadrant.
9000014206 Level: BFind the domain \(\mathrm{Dom}(f)\) and range \(\mathop{\mathrm{Ran}}(f)\) of the function \(f(x) = \frac{2+x} {x+4}\).\begin{align*} \mathrm{Dom}(f) &= (-\infty ;-4)\cup (-4;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}\begin{align*} \mathrm{Dom}(f) &= (-\infty ;4)\cup (4;\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}\begin{align*} \mathrm{Dom}(f) &= (-\infty ;2)\cup (2;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;4)\cup (4;\infty ) \end{align*}\begin{align*} \mathrm{Dom}(f) &= (-\infty ;4)\cup (4;\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;2)\cup (2;\infty ) \end{align*}
9000014207 Level: BIdentify a possible analytic expression for the function \(f\) graphed in the picture.\(f(x)= \frac{x+1} {x+2}\)\(f(x)= \frac{1} {x+2} - 1\)\(f(x) = \frac{1} {x+2} + 1\)\(f(x) = \frac{x+1} {x-2}\)
9000014208 Level: BIdentify a possible analytic expression for the function \(f\) graphed in the picture.\(f(x) = \frac{2x+1} {x-1} \)\(f(x) = \frac{3} {x-1} - 2\)\(f(x)= \frac{2x-1} {x+1} \)\(f(x) = \frac{2x+2} {x-1} \)