Power and radical functions

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]

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]

1103161003

Level:

The graphs represent the parts of the functions

f (x) = x^{- 2}

and

g (x) = x^{- 3}

. Identify which of the following inequalities has the solution set

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

- x^{- 3} < x^{- 2}

| x^{- 3} | < x^{- 2}

x^{- 3} < - x^{- 2}

x^{- 3} < | x^{- 2} |

1103161002

Level:

The graphs represent the parts of the functions

f (x) = x^{- 2}

and

g (x) = x^{- 4}

. Identify which of the following inequalities has the solution set

(- \infty; - 1] \cup [1; \infty)

x^{- 4} \leq x^{- 2}

x^{- 2} \leq x^{- 4}

x^{- 2} > x^{- 4}

x^{- 2} < 1

1103161001

Level:

The graphs represent the parts of the functions

f (x) = x^{- 2}

and

g (x) = x^{- 3}

. Identify which of the following statements is false.

The solution set of the inequality

x^{- 2} > 0

(- \infty; \infty)

The solution set of the inequality

x^{- 3} > 0

(0; \infty)

The solution set of the equation

x^{- 3} = x^{- 2}

{1}

The solution set of the inequality

x^{- 3} < x^{- 2}

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

1103159303

Level:

The graphs represent the parts of the functions

f (x) = x^{- 2}

and

g (x) = x^{- 3}

. Identify which of the following statements is true.

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

(- 2)^{- 2} \leq - 2^{- 2}

(- 2)^{- 3} < - 2^{- 3}

(- 2)^{- 3} \leq - 2^{- 2}

1103159302

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.

{(\frac{1}{2})}^{- 3} < {(\frac{1}{2})}^{- 4}

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

(- 2)^{- 4} \leq (- 2)^{- 3}

(- 1)^{- 4} > 1^{- 3}

1103159301

Level:

The graphs represent the parts of the functions

f (x) = x^{- 2}

and

g (x) = x^{- 3}

. Identify which of the following statements is false.

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

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

{(- \frac{1}{2})}^{- 2} \geq (- 2)^{- 2}

(- 2)^{- 2} \geq 2^{- 2}

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

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}

Power and radical functions

1103163102

1103163101

1103161003

1103161002

1103161001

1103159303

1103159302

1103159301

1003162203

1003162202

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