9100003210
Level:
B
Identify a possible graph of the function
\(f(x) = -2 - \frac{1}
{x-1}\).
Rational functions
9100014204
Level:
B
Identify a possible graph for the function
\(f(x) = \frac{2}
{x+1} - 1\).
9100014205
Level:
B
Identify a possible graph for the function
\(f(x) = 2 - \frac{1}
{x-3}\).
1003019401
Level:
C
Identify which of the given functions is even.
\( m(x)=\frac{x^4-3}{x^2} \)
\( h(x)=\frac{x^3+2}{x^2} \)
\( g(x)=\frac{x^2}{x+1} \)
\( f(x)=\frac{x^3}{x^2-5} \)
1003019402
Level:
C
Identify which of the given functions is neither even nor odd.
\( h(x) = \frac{x^3-7}{2x^2} \)
\( f(x) = \frac{x^2+3}{3x^4} \)
\( g(x) = \frac{5x^2-6}{x} \)
\( m(x) = \frac{x^3}{2x^2+5} \)
1003028401
Level:
C
Let \( f(x)=\frac{3x-9}{x^2-3} \). Which of the statements about the domain and the range of the function \( f \) is true?
\( 3\in D(f) \wedge 3\in H(f) \)
\( 3\in D(f) \wedge 3\notin H(f) \)
\( 3\notin D(f) \wedge 3\in H(f) \)
\( 3\notin D(f) \wedge 3\notin H(f) \)
1003028402
Level:
C
Let \( f(x)=\frac{2x-4}{x^2-4} \). Which of the statements about the domain and the range of the function \( f \) is true?
\( -2\notin D(f) \wedge -2\in H(f) \)
\( -2\in D(f) \wedge -2\notin H(f) \)
\( -2\in D(f) \wedge -2\in H(f) \)
\( -2\notin D(f) \wedge -2\notin H(f) \)
1003030903
Level:
C
Identify which of the following functions is bounded below.
\( h(x)=\frac{2x-4}{x-2} \)
\( m(x)=\frac{x^2-4}{x-2} \)
\( g(x)=\frac{4-x^2}{x-2} \)
\( f(x)= -\left|\frac{x^2-4}{x-2}\right| \)
1003118304
Level:
C
Identify which of the following functions is bounded.
\( h(x)=\frac{3x-6}{2x-4} \)
\( f(x)=\frac{3x-6}{2x} \)
\( g(x)=3-\frac6{2x} \)
\( m(x)=\left|\frac{4x-3}{2x-6}\right| \)
1003118305
Level:
C
Find the false statement about the function \( f(x)=\left|\frac1{2-3x}-3\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac32\right)\cup\left(\frac32;\infty\right) \).
The range of the function \( f \) is the interval \( \left[0;\infty\right) \).
The function \( f \) has the minimum at \( x=\frac59 \).
The function \( f \) is bounded below.