Analyzing function behavior

2010020005

Level:

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 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.

2110020003

Level:

A function \(f\) is given by the formula \(f(x)=(x+3)^3-3x-6\). Choose the picture that shows a part of the graph of this function.

2010020002

Level:

A function \(f\) is given by the formula \[f(x)=1-\sqrt{\frac{x^4}{4}-4x^2+16}.\] Choose the true statement about local extrema of this function.

The function has two local maxima and one local minimum.

The function has two local minima and one local maximum.

The function has two local minima and no local maximum.

The function has two local maxima and no local minimum.

2010020001

Level:

A function \(f\) is given by the formula \[f(x)=1+\sqrt{\frac{x^4}{4}-2x^2+4}.\] Choose the true statement about local extrema of this function.

The function has two local minima and one local maximum.

The function has two local maxima and one local minimum.

The function has two local minima and no local maximum.

The function has two local maxima and no local minimum.

2010013910

Level:

Suppose a function is increasing on the interval \([-6;-3]\). Which one of the offered functions has that property?

\(i(x)=-x^4+2x^2-3\)

\(h(x)=\sqrt{x^2+x}+1\)

\(f(x)=\frac{1-x^2}{x}\)

\(g(x)=(x+3)^3-3x-6\)

2010013909

Level:

Suppose a function is decreasing on the interval \([-5;-2]\). Which one of the offered functions has that property?

\(h(x)=\frac{x^4}{2}-x^2-1\)

\(f(x)=2-\sqrt{x^2+x}\)

\(g(x)=\frac{x^2+3}{x}\)

\(i(x)=(x+2)^3-x-1\)

2010013908

Level:

How many of the given functions have exactly one inflection point? \[\] \(f(x)=\frac1{-2(x+4)^4}+6,\) \(g(x)=-(x-3)^5-(-3+x)^3+1,\) \(h(x)=\frac{x^3-3x^2+6x+9}{-3x}\)

None of these functions has exactly one inflection point.

2010013907

Level:

How many of the given functions have exactly one inflection point? \[\] \(f(x)=(x+2)^5+(2+x)^3-2,\) \(g(x)=\frac1{6(x+4)^4},\) \(h(x)=\frac{x^3+2x^2+x+2}{x}\)

None of these functions has exactly one inflection point.

2010013906

Level:

Suppose a function is convex up on the interval \([-2;1]\). Which one of the offered functions has that property?

\(h(x)=-\sqrt{x+5}\)

\(f(x)=\frac{x-2}{(x+5)^2}\)

\(g(x)=\frac{x^2-2}{2x}\)

\(k(x)=-\frac15x^3-2x^2+x+1\)

Analyzing function behavior

2010020005

2110020004

2110020003

2010020002

2010020001

2010013910

2010013909

2010013908

2010013907

2010013906

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