Analyzing function behavior
2010020012
Level:
C
How many of the following functions have exactly two asymptotes?
\[\]
\(f(x)=\frac{-x^3+1}{(x-3)^2},\) \(h(x)=\left(\frac{x+2}{x-2}\right)^4,\) \(i(x)=-\frac{x^2}{x^2-2},\) \(g(x)=\sqrt{6x+2}\)
2
1
3
None of these functions has exactly two asymptotes.
2010020011
Level:
C
How many of the following functions have exactly two asymptotes?
\[\]
\(f(x)=\left(\frac{4+x}{4-x}\right)^4,\) \(g(x)=\frac{x^3}{(x-2)^2},\) \(h(x)=\sqrt{6-4x},\) \(i(x)=\frac{x^2}{4-x^2}\)
2
1
3
None of these functions has exactly two asymptotes.
2010020010
Level:
C
A function \(f\) is given by the formula \(f(x)=\frac{1+\ln{x}}{x^2-3}\). For the function \(f\) identify all vertical asymptotes.
\(x=\sqrt3,\quad x=0\)
\(x=\sqrt3,\quad x=-\sqrt3,\quad x=0\)
\(x=\sqrt3,\quad x=-\sqrt3\)
This function has no vertical asymptote.
2010020009
Level:
C
A function \(f\) is given by the formula \(f(x)=\frac{\ln{x}}{2-x^2}\). For the function \(f\) identify all vertical asymptotes.
\(x=\sqrt2,\quad x=0\)
\(x=\sqrt2,\quad x=-\sqrt{2},\quad x=0\)
\(x=\sqrt2,\quad x=-\sqrt{2}\)
This function has no vertical asymptote.
2010020008
Level:
C
A function \(f\) is given by the formula \(f(x)=\frac{3x^2-1}{x-2}\). For the function \(f\) identify a slant or horizontal asymptote.
\(y=3x+6\)
\(y=3\)
\(y=3x-3\)
This function has neither horizontal nor slant asymptote.
2010020007
Level:
C
A function \(f\) is given by the formula \(f(x)=\frac{2x^2+3}{x+1}\). For the function \(f\) identify a slant or horizontal asymptote.
\(y=2x-2\)
\(y=2\)
\(y=-2x\)
This function has neither horizontal nor slant asymptote.
2010020006
Level:
C
The picture shows the part of the graph of a function \(f\). Choose the formula of the function \(f\) whose graph corresponds to this picture.
\(f(x)=-\frac{x^2}{4-x^2}-1\)
\(f(x)=\frac{x^2+4}{x^2-4}\)
\(f(x)=\frac{x}{x^2-4}+1\)
\(f(x)=\frac{x^2}{4-x^2}\)
2010020005
Level:
C
The picture shows the part of the graph of a function \(f\). Choose the formula of the function \(f\) whose graph corresponds to this picture.
\(f(x)=\frac{x^2+4}{x^2-4}\)
\(f(x)=\frac{x}{x^2-4}+1\)
\(f(x)=-\frac{x^2}{4-x^2}-1\)
\(f(x)=\frac{x^2}{4-x^2}\)
2110020004
Level:
A
A function \(f\) is given by the formula \(f(x)=-(x-3)^3+3x-12\). Choose the picture that shows a part of the graph of this function.
