Exponential functions

1103024908

Level:

The graphs of functions

f (x) = a \cdot 2^{b x} + 2

, where

a \in {- 1, 1}

b \in {- 1, 1}

, are below. Identify which of the graphs represents the function that is increasing, bounded below, and has an asymptote at

y = 2

2010010201

Level:

Which values of the real parameter

p

ensure that the function

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

is an increasing function?

p \in (- \infty; - 5)

p \in R

p \in (- \infty; - 5) \cup (2; \infty)

p \in (- 5; - 2)

2010010202

Level:

Using properties of exponential function convert the following inequality to an explicit inequality for the parameter

a

{(\sqrt{5} - \sqrt{3})}^{a + 2} > {(\sqrt{5} - \sqrt{3})}^{4 a - 1}

a > 1

a < 1

a > 0

0 < a < 1

2010013001

Level:

Consider values

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

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

1

2

4

3

1

2010013002

Level:

For what values of the parameter

a

is the exponential function

f (x) = (2 a + 3)^{x}

increasing?

a > - 1

a > - 1.5

a < - 1

- 1.5 < a < - 1

2010013003

Level:

For what values of the parameter

a

is the exponential function

f (x) = (2 a + 1)^{x}

decreasing?

- 0.5 < a < 0

- 1.5 < a < 1

a < - 1

a > - 0.5

2010013010

Level:

Given the functions

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

and

g (x) = {(\frac{1}{2})}^{x} - 3

, specify the quadrant of the coordinate system to which the point of intersecion of their graphs belongs.

I I I

I V

I

I I

2010013011

Level:

Given the functions

f (x) = 3^{x - 5} - 2

and

g (x) = {(\frac{1}{3})}^{x + 1} - 2

, specify the quadrant of the coordinate system to which the point of intersection of their graphs belongs.

I V

I I I

I I

I

2010013014

Level:

Let

f

be a function defined by

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

, where

m

is a parameter. Which of the following statements about the function

f

and the line

y = 3

is true?

The graph of

f

and the line have always a common point for all

m \in (- 3; \infty)

The graph of

f

and the line have always a common point for

m = - 3

The graph of

f

and the line have always a common point for all

m \in (- \infty; - 3)

The graph of

f

and the line have always a common point for all

m \in R

2010013015

Level:

Let

f

be a function defined by

f (x) = 2^{x + m} + m

, where

m

is a parameter. Which of the following statements about the function

f

and the line

y = - 3

is true?

The graph of

f

and the line have always a common point for all

m \in (- \infty; - 3)

The graph of

f

and the line have always a common point for

m = - 3

The graph of

f

and the line have always a common point for all

m \in (- 3; + \infty)

The graph of

f

and the line have always a common point for all

m \in R

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