Exponential functions

1003024903

Level:

Given the function

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

, where

a < 0

and

0 < b < 1

, find the correct statement.

Function

f

is increasing.

Function

f

is decreasing.

Function

f

is nonincreasing.

Function

f

is nondecreasing.

1003024904

Level:

Which of the following functions is decreasing?

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

f (x) = - 5^{- x}

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

f (x) = 5^{x}

1003024905

Level:

Which of the following functions is bounded above?

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

f (x) = {(\frac{1}{3})}^{- x}

f (x) = 3^{x}

f (x) = {(\frac{1}{3})}^{x}

1003024907

Level:

Choose the correct list of properties of the function

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

decreasing, bounded above, asymptote at

y = 0

decreasing, bounded below, asymptote at

x = 0

increasing, bounded below, asymptote at

x = 0

increasing, bounded below, asymptote at

y = 0

1103019601

Level:

Consider values

{0.7}^{- 0.5}; {(\frac{5}{8})}^{6}; {(\frac{3}{2})}^{- 5}; {3.5}^{0}; {0.4}^{4}; 5^{3} .

Determine how many of the values are greater than

1

. Use the graph of an exponential function given below.

2

4

3

1

1103019603

Level:

Identify which of the relations between

m

and

n

ensures

{(\frac{12}{7})}^{m} < {(\frac{12}{7})}^{n}

. Use the graph of

f (x) = {(\frac{12}{7})}^{x}

given below.

m < n

m > n

m = n

m \geq n

1103019604

Level:

What are the values of the real variable

x

, if

{0.7}^{x} \leq 1

? Use the graph of

f (x) = {0.7}^{x}

given below.

x \in [0; \infty)

x \in (- \infty; 0)

x \in (- \infty; 0]

x \in (0; \infty)

1103019605

Level:

What are the values of the real variable

x

, if

5^{x} \leq 1

? Use the graph of

f (x) = 5^{x}

given below.

x \in (- \infty; 0]

x \in [0; \infty)

x \in (- \infty; 0)

x \in (0; \infty)

1103019606

Level:

Identify which of the following relations is correct. Use the graph of

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

given below.

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

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

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

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

1103024906

Level:

The graph of function

- 3^{- x}

is below. Choose the correct list of properties of

f

increasing, bounded above, asymptote at

y = 0

decreasing, bounded above, asymptote at

y = 0

decreasing, bounded below, asymptote at

x = 0

increasing, bounded below, asymptote at

x = 0

1003024903

1003024904

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1103024906

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