Rational functions
2000018804
Level:
A
Given the function \(f(x) = -\frac{4}
{x}\),
find the function \(g\) such
that the graphs of \(f\)
and \(g\) are symmetric
about the \(y\)-axis.
\(g(x) = \frac{4}
{x}\)
\(g(x) =4
{x}\)
\(g(x) = -\frac{4}
{x}\)
\(g(x) = -{4}
{x}\)
2000018805
Level:
A
The test driver drove from Ostrava to Warsaw at an average speed of \(66\, \mathrm{km}/\mathrm{h}\) and the journey took him \(6\) hours. After him, the same route took several other drivers. (Each driver took a different driving time.) Choose the function giving the average speed \(v\) of each of these drivers as a function of the total driving time \(t\) from Ostrava to Warsaw.
\( v=\frac{396}t,\ \ t\in(0;\infty) \)
\( v=\frac{66}t,\ \ t\in(0;\infty) \)
\( v=66 t,\ \ t\in(0;\infty) \)
\( v=\frac{t}{396},\ \ t\in(0;\infty) \)
2000018803
Level:
A
Given the function \(f(x) = \frac{5}
{x}\),
find the function \(g\) such
that the graphs of \(f\)
and \(g\) are symmetric
about the line \(y = -x\).
\(g(x) = \frac{5}
{x}\)
\(g(x) =5
{x}\)
\(g(x) = -\frac{5}
{x}\)
\(g(x) = -{5}
{x}\)
2000018802
Level:
A
Given the function \(f(x)= \frac{6}
{x} \),
evaluate \( \frac{f(-3)}{ f(2)}\).
\(-\frac23\)
\(-6\)
\(-\frac32\)
\(-\frac16\)
2000018801
Level:
A
Consider a triangle with area of
\(5\, \mathrm{cm}^{2}\). Find the formula which relates the length of its side \(a\) to the length of the height \(v_a\) , where \(v_a\) is the height to the side \(a\).
\(v_a = \frac{10}
{a}\)
\(v_a = \frac{5}
{a}\)
\(v_a =5
{a}\)
\(v_a = \frac{5}
{2a}\)
2110017303
Level:
C
Let \( f(x)=\frac{x^2-1}{x^2-3x+2} \). One of the following pictures shows a part of the graph of \( f \). Choose the picture.
2010017305
Level:
C
The picture shows parts of the graphs of the functions
\[
\text{$f(x)= \frac{k_{1}}
{x} $ and $g(x) = \frac{k_{2}}
{x} $.}
\]
Find the relationship between \(k_{1}\)
and \(k_{2}\)?
\( k_1 < k_2\)
\( k_1 \geq k_2\)
\( k_1 = k_2\)
The relationship between \(k_1\) and \(k_2\) cannot be determined from the picture.
2010017304
Level:
C
Consider the functions
\[
\text{$f(x)= -\frac{2}
{3x}$ and $g(x) = \frac{k}
{x}$.}
\]
Identify the value of the coefficient \(k\)
which ensures that the graphs of both functions are symmetric about
\(y\)-axis.
\( k=\frac23\)
\( k=\frac32\)
\( k=-\frac23\)
\( k=-\frac32\)
2010017302
Level:
C
Find the interval where the function \(f(x) = -\left |2+\frac{1}
{x}\right |\) is a decreasing
function. The function \(f\)
is graphed in the picture.
\(\left[ -\frac12; 0\right)\)
\((-\infty ;0)\)
\(\left[ -\frac12; \infty\right)\)
\(\left(-\infty ; -\frac12\right)\)