1103030407
Level:
C
Suppose function \( f \) is given by the graph. Identify which of the following graphs is the graph of the inverse of \( f \).
Properties of Functions
1003030406
Level:
C
Identify which of the following functions is the inverse of function \( f(x)=\frac{2x+1}{x-3 }\).
\( h(x)=\frac{3x+1}{x-2} \)
\( g(x)=\frac{x-3}{2x+1} \)
\( m(x)=\frac{2x-1}{x+3} \)
\( n(x)=\frac{3x-1}{x+2} \)
1003030405
Level:
C
Identify which of the following functions is the inverse of function \( f(x)=-\frac12 x+3 \).
\( h(x)=-2x+6 \)
\( g(x)=-2x+3 \)
\( m(x)=-2x+\frac13 \)
\( n(x)=\frac12 x-3 \)
1003030404
Level:
C
Identify which of the following points lies on the graph of the inverse of function \( f(x)=x^3+2 \).
\( [-6;-2] \)
\( [6;2] \)
\( [-2;-6] \)
\( [-6;2] \)
\( [-2;6] \)
1003030403
Level:
C
Identify which of the following functions is not an injective (one-to-one) function.
\( m(x)=|x-2|;\ x\in[-2; 3 ) \)
\( h(x)=x^3+3;\ x\in[-2;3) \)
\( g(x)=(x+2)^2;\ x\in[-2; 3) \)
\( f(x)= \frac{x+2}{x-3};\ x\in[-2; 3) \)
1003030402
Level:
C
Suppose function \( f \) is given completely by the next table.
\[
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline f(x)&-1&2&-3&1&-2&3&2 \\\hline
\end{array}\]
Identify which of the following statements is true.
The inverse of \( f \) does not exist.
The inverse of \( f \) is function \( h \), which is given completely by the next table.
\(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-1&2&-3&1&-2&3&2 \\\hline h(x)&-3&-2&-1&0&1&2&3 \\\hline
\end{array}
\)
The inverse of \( f \) is function \( g \), which is given completely by the next table. \(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline g(x)&1&-2&3&-1&2&-3&-2 \\\hline
\end{array}\)
The inverse of \( f \) is function \( m \), which is given completely by the next table. \(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&3&2&1&0&-1&-2&-3 \\\hline m(x)&1&-2&3&-1&2&-3&-2 \\\hline
\end{array}\)
1003030401
Level:
C
Suppose function \( f \) is given completely by the next table.
\[
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline f(x)&-1&0&1&2&3&4&5 \\\hline
\end{array}\]
Identify which of the following functions is the inverse of \( f \).
Function \( h \), which is given completely by the next table.
\(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-1&0&1&2&3&4&5 \\\hline h(x)&-3&-2&-1&0&1&2&3 \\\hline
\end{array}\)
Function \( m \), which is given completely by the next table.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline m(x)&5&4&3&2&1&0&-1 \\\hline
\end{array}\)
Function \( g \), such that \( g(x)=x-2 \) for \( x\in[-1;5] \).
Function \( n \), such that \( n(x)=x+2 \) for \( x\in[-3;3] \).
1003030807
Level:
B
The function \( f(x) \) is increasing in the interval \( J \). Identify which of the following statements is false.
The function \( h(x) = -2 f(x) \) is increasing in the interval \( J \).
The function \( g(x) = 2 f(x) \) is increasing in the interval \( J \).
The function \( m(x) = f(x)+2 \) is increasing in the interval \( J \).
The function \( n(x) = f(x)-2 \) is increasing in the interval \( J \).
1103030806
Level:
A
The function \( f \) is given by the graph. Identify which of the following statements is false.
The function \( f \) is non-increasing in the interval \( [ -3;2 ] \).
The function \( f \) is not increasing.
The function \( f \) is decreasing in the interval \( [ 2;5 ] \).
The function \( f \) is non-decreasing in the interval \( [ -1;2 ] \).
1003030805
Level:
B
Identify which of the following functions is increasing in the interval \( [ 1;\infty ) \).
\( m(x)=(1-x)^2 \)
\( g(x)=1-x \)
\( h(x)=1-x^2 \)
\( f(x)=1-x^3 \)