Power and radical functions

1003154401

Level:

Find the true statement about the function

f (x) = 2 - (x - 1)^{3}

The function

f

is an injective (one-to-one) function.

The function

f

is increasing.

The function

f

is odd.

The function

f

has the maximum at

x = 1

1003154402

Level:

Find the false statement about the function

f (x) = 3 - (x + 2)^{4}

The function

f

is even.

The function

f

has the maximum at

x = - 2

The function

f

is bounded above.

The range of the function

f

is the interval

(- \infty; 3]

1003162201

Level:

Let

f (x) = x^{- 2}

. Identify which of the following statements is false.

f (\frac{2}{3}) = \frac{4}{9}

f (- 0.125) = 64

f (\frac{1}{4}) = 16

f (\frac{1}{0.5}) = \frac{1}{4}

1003162202

Level:

Let

f (x) = x^{- 3}

. Identify which of the following statements is true.

f (- \frac{2}{3}) = - \frac{27}{8}

f (0) = 1

f (- \frac{1}{10}) = - 0.001

f (0.2) = \frac{1}{125}

1003162203

Level:

Let

f (x) = x^{- 2}

and

g (x) = x^{- 3}

. Identify which of the following statements is false.

f (2) + g (2) = \frac{1}{32}

f (2) \cdot g (2) = \frac{1}{32}

\frac{f (2)}{g (2)} = 2

f (2^{- 3}) = 64

1103143401

Level:

The graphs represent the parts of the functions

f (x) = x^{3}

and

g (x) = x^{4}

. Identify which of the following statements is false.

{(- \frac{1}{2})}^{3} > (2)^{3}

(- 2)^{3} < {(- \frac{1}{2})}^{3}

{(\frac{1}{3})}^{3} \geq (0.3)^{3}

(- 1)^{3} \leq (1)^{3}

1103143402

Level:

The graphs represent the parts of the functions

f (x) = x^{3}

and

g (x) = x^{4}

. Identify which of the following statements is true.

(- 3)^{4} > (2)^{4}

(- 2)^{4} < {(- \frac{1}{2})}^{4}

{(- \frac{1}{4})}^{4} \geq (0.3)^{4}

(- 1)^{4} < (1)^{4}

1103143403

Level:

The graphs represent the parts of the functions

f (x) = x^{3}; g (x) = x^{4}; h (x) = x^{5}

. Identify which of the following statements is false.

{(- \frac{1}{3})}^{5} < {(- \frac{1}{3})}^{3}

{(\frac{1}{2})}^{5} < {(- \frac{1}{2})}^{4}

(- 3)^{4} > (3)^{3}

{(\frac{1}{4})}^{3} \geq (- 0.25)^{4}

1103143501

Level:

The graphs represent the parts of the functions

f (x) = x^{3}

and

g (x) = x^{4}

. Identify which of the following statements is false.

The solution set of the inequality

x^{4} > x^{3}

(1; \infty)

The solution set of the inequality

x^{4} > 0

(- \infty; 0) \cup (0; \infty)

The solution set of the equation

x^{3} = x^{4}

{0; 1}

The solution set of the inequality

x^{3} \geq x^{4}

[0; 1]

1103143502

Level:

The graphs represent the parts of the functions

f (x) = x^{3}

and

g (x) = x^{5}

. Identify which of the following inequalities has the solution set

(- 1; 0) \cup (1; \infty)

x^{3} < x^{5}

x^{5} \geq x^{3}

x^{3} > x^{5}

x^{3} > - 1

Power and radical functions

1003154401

1003154402

1003162201

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1003162203

1103143401

1103143402

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1103143501

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