Exponential functions

9100003606

Level:

Identify a possible graph of the following function.

f (x) = {(\frac{2}{5})}^{x + 2} - 1

1003019602

Level:

Consider values

4^{5}; {0.2}^{\frac{1}{2}}; {(\frac{5}{4})}^{0}; {(\frac{1}{3})}^{- 3}; {(\frac{7}{6})}^{- 3}; {2.5}^{0.6} .

Without using a calculator, determine how many of the values are less than

1

2

4

3

1

1003019607

Level:

Which of the relations between

m

and

n

ensures

{(\frac{4}{5})}^{m} < {(\frac{4}{5})}^{n}

m > n

m \geq n

m = n

m < n

1003019608

Level:

Which of the relations between

m

and

n

ensures

{(\frac{5}{4})}^{m} < {(\frac{5}{4})}^{n}

m < n

m \geq n

m = n

m > n

1003019609

Level:

What are the values of the real

a

, that satisfy inequality

a^{\frac{2}{5}} > a^{\frac{4}{5}}

0 < a < 1

a > 1

a < 1

a > 0

1003019610

Level:

What are the values of the real

a

, that satisfy inequality

a^{- 3} > a^{- 2}

0 < a < 1

a > 1

a < 1

a > 0

1003019611

Level:

Identify which of the following relations is correct.

{(\frac{1}{5})}^{- 6} > {(\frac{1}{5})}^{- \frac{2}{3}} > {(\frac{1}{5})}^{\frac{2}{5}} > {(\frac{1}{5})}^{2} > {(\frac{1}{5})}^{7}

{(\frac{1}{5})}^{7} > {(\frac{1}{5})}^{2} > {(\frac{1}{5})}^{\frac{2}{5}} > {(\frac{1}{5})}^{- \frac{2}{5}} > {(\frac{1}{5})}^{- 6}

{(\frac{1}{5})}^{- \frac{2}{3}} > {(\frac{1}{5})}^{- 6} > {(\frac{1}{5})}^{\frac{2}{5}} > {(\frac{1}{5})}^{2} > {(\frac{1}{5})}^{7}

{(\frac{1}{5})}^{- 6} > {(\frac{1}{5})}^{- \frac{2}{3}} > {(\frac{1}{5})}^{\frac{2}{5}} > {(\frac{1}{5})}^{7} > {(\frac{1}{5})}^{2}

1003019612

Level:

Identify which of the following relations is correct.

2^{7} > 2^{2} > 2^{\frac{2}{5}} > 2^{- \frac{2}{5}} > 2^{- 6}

2^{- 6} > 2^{- \frac{2}{3}} > 2^{\frac{2}{5}} > 2^{2} > 2^{7}

2^{- \frac{2}{3}} > 2^{- 6} > 2^{\frac{2}{5}} > 2^{2} > 2^{7}

2^{- 6} > 2^{- \frac{2}{3}} > 2^{\frac{2}{5}} > 2^{7} > 2^{2}

1003024901

Level:

Given the increasing exponential function

f (x) = a^{x}

, choose the correct statement about the base

a

a > 1

a = 1

a < 1

0 < a < 1

1003024902

Level:

Given the function

f (x) = a \cdot b^{x}

, where

a < 0

and

b > 0

, find the correct statement.

Function

f

is bounded above.

Function

f

is bounded below.

Function

f

is bounded.

Function

f

is unbounded.

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