Power and Radical Functions

1103163101

Level:

Function \( f \) is given by the graph. Identify which of the following statements is true.

\( f(x)=2+(x-1)^{-2},\ x\in[1.5,6] \)

\( f(x)=2+(x-2)^{-2},\ x\in[1.5,6] \)

\( f(x)=2+(x-1)^2,\ x\in[1.5,6] \)

\( f(x)=2+(x-1)^{-1},\ x\in[1.5,6] \)

1103163102

Level:

Function \( f \) is given by the graph. Identify which of the following statements is true.

\( f(x)=(x+1)^{-3},\ x\in[-3,-1.5] \)

\( f(x)=-(x+1)^{-2},\ x\in[-3,-1.5] \)

\( f(x)=(x+1)^{-5},\ x\in[-3,-1.5] \)

\( f(x)=(x+1)^{-1},\ x\in[-3,-1.5] \)

The parts of the graphs represent the functions: \( f(x)=x^{-2} \), \( g(x)=x^{-3} \), \( h(x)=x^{-4} \). Choose the legend which assigns the correct color of the graph to each of the given functions.

\( f \) -- green, \( g \) -- blue, \( h \) -- red

\( f \) -- red, \( g \) -- blue, \( h \) -- green

\( f \) -- green, \( g \) -- red, \( h \) -- blue

\( f \) -- blue, \( g \) -- green, \( h \) -- red

2010012401

Level:

Identify a function which is increasing on \((-1,\infty )\).

\(f\colon y = x^{3}\)

\(f\colon y= x^{4}\)

\(f\colon y= -x^{3}\)

\(f\colon y = x^{-4}\)

\(f\colon y =- x^{-2}\)

\(f\colon y = -x^{-3}\)

2010012402

Level:

Identify a function which is decreasing on \((-3,2 )\).

\(f \colon y = (x - 2)^{2}\)

\(f \colon y = (x + 2)^{2}\)

\(f \colon y = (x +3)^{2}\)

\(f \colon y = x^{2}-2x\)

\(f \colon y =-x^{2}+1\)

\(f \colon y = x^{3}\)

2010012403

Level:

Identify a function which is not one-to-one on the interval \([ - 2,2 ] \).

\(f \colon y = x^{2}-2\)

\(f \colon y = x^{2}+4x\)

\(f \colon y = -x^{3}\)

\(f \colon y = (x - 2)^{2}\)

\(f \colon y = (x +2)^{2}\)

\(f \colon y = x^{3}-2\)

2010012404

Level:

In the following list identify a decreasing function.

\(f \colon y =-x^{3}\)

\(f \colon y = x^{4}\)

\(f \colon y = -x^{4}\)

\(f \colon y = x^{-3}\)

\(f \colon y = -x^{2}\)

2010012405

Level:

Find the true statement about the function \( f(x)=(x+1)^3-2 \).

The function \( f \) is an injective (one-to-one) function.

The function \( f \) is decreasing.

The function \( f \) is odd.

The function \( f \) has the minimum at \( x=-1 \).

2010012406

Level:

Find the false statement about the function \( f(x)=(x-2)^4-3 \).

The function \( f \) is even.

The function \( f \) has the minimum at \( x=2 \).

The function \( f \) is bounded below.

The range of the function \( f \) is the interval \( [ -3,\infty) \).

9000010605

Level:

Identify a function which is decreasing on \((-\infty ,1)\).

\(f(x) = -x^{3}\)

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

\(f(x) = x^{3}\)

\(f(x) = -x^{4}\)

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

\(f(x) = x^{2}\)

Power and Radical Functions

1103163101

1103163102

1103163103

2010012401

2010012402

2010012403

2010012404

2010012405

2010012406

9000010605

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