Exponential functions

2010013012

Level:

Find the formula of an exponential function

f (x) = a^{x}

, if you know that the point

P = [- \frac{1}{2}; 8]

lies on its graph.

f (x) = {(\frac{1}{64})}^{x}

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

f (x) = {(\frac{1}{8})}^{x}

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

2010013013

Level:

Find the formula of an exponential function

f (x) = a^{x}

, if you know that the point

P = [- \frac{1}{2}; 7]

lies on its graph.

f (x) = {(\frac{1}{49})}^{x}

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

f (x) = {(\frac{1}{7})}^{x}

f (x) = {(- \frac{1}{7})}^{x}

2010013018

Level:

By what vector

\vec{u}

should the graph of the function

f (x) = {(\frac{1}{4})}^{x - 2} + 3

be translated to get the graph of the function

f (x) = 4^{5 - x} - 1

\vec{u} = (3; - 4)

\vec{u} = (- 3; - 4)

\vec{u} = (3; 4)

\vec{u} = (- 3; 4)

2010013019

Level:

By what vector

\vec{u}

should the graph of the function

f (x) = {(\frac{1}{4})}^{5 - x} - 1

be translated to get the graph of the function

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

\vec{u} = (- 3; 4)

\vec{u} = (- 3; - 4)

\vec{u} = (3; 4)

\vec{u} = (3; - 4)

2010013020

Level:

By what vector

\vec{u}

should the graph of the function

f (x) = 5^{x + 1} - 6

be translated to get the graph of the function

f (x) = {(\frac{1}{5})}^{3 - x} - 4

\vec{u} = (4; 2)

\vec{u} = (- 4; - 2)

\vec{u} = (4; - 2)

\vec{u} = (- 4; 2)

2010013021

Level:

By what vector

\vec{u}

should the graph of the function

f (x) = 5^{3 - x} - 4

be translated to get the graph of the function

f (x) = {(\frac{1}{5})}^{x + 1} - 6

\vec{u} = (- 4; - 2)

\vec{u} = (4; 2)

\vec{u} = (4; - 2)

\vec{u} = (- 4; 2)

2110010205

Level:

Which of the given graphs is the graph of the function

f (x) = 5 \cdot {0.2}^{- x}

9000003701

Level:

Identify a possible analytic expression for the exponential function graphed in the picture.

y = 2^{x - 1} - 2

y = 2^{x + 1} - 2

y = 2^{x + 1} + 2

y = 2^{x - 1} + 2

9000003702

Level:

In the following list identify a function whose graph passes through the points

[3; 0]

and

[5; 3]

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

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

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

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

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

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

9000003703

Level:

In the following list identify a point which is not on the graph of the function

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

C = [- 2; 6]

A = [- 1; 0]

B = [1; \frac{8}{3}]

D = [0; 2]

E = [- 3; - 24]

F = [2; \frac{26}{9}]

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