Logarithmic functions

9000004909

Level:

Identify a possible analytic expression for the function

g

graphed in the picture.

y = \log_{3} (x + 2) - 1

y = \log_{\frac{1}{3}} (x + 2) - 1

y = \log_{3} (x - 2) + 1

y = \log_{\frac{1}{3}} (x - 2) + 1

9000004808

Level:

In the following list identify a function which is bounded below.

y = 3^{x}

y = - 3^{x}

y = \log_{3} x

y = - \log_{3} x

9000004905

Level:

In the following list identify a statement which is not true for the function

f : y = | \log (x - 3) - 1 |

The function

f

is increasing on the domain.

The domain of the function

f

(3; \infty)

All values of the function

f

are nonnegative.

The function

f

does not have a

y

-intercept.

The

x

-intercept of the function

f

x = 13

The function

f

is not one-to-one.

9000004902

Level:

Find the domain of the function

f : y = \log_{\frac{1}{3}} (9 - x^{2})

Dom (f) = (- 3; 3)

Dom (f) = R ∖ {3}

Dom (f) = (- \infty; 3)

Dom (f) = (3; \infty)

Dom (f) = (- \infty; - 3) \cup (3; \infty)

9000003801

Level:

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

y = \log_{\frac{1}{2}} (x + 1) + 1

y = \log_{\frac{1}{2}} (x - 1) + 1

y = \log_{\frac{1}{2}} (x - 1) - 1

y = \log_{\frac{1}{2}} (x + 1) - 1

9000003803

Level:

The function

g : y = \log_{3} (x - 2)

is graphed in the picture. In the following list identify a false statement.

The function

g

is a positive function.

The domain of the function

g

is the interval

(2; \infty)

The function

g

is not bounded.

The function

g

is an increasing function.

The function

g

has neither minimum nor maximum.

The graph of the function

g

goes through

[5; 1]

9000003804

Level:

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

f (x) = 1 - \log_{3} x

[0; 1]

[3; 0]

{[\frac{1}{9}; 3]}_{}

[1; 1]

[\frac{1}{3}; 2]

[9; - 1]

9000003807

Level:

In the following list identify a negative expression.

\log_{0.1} 20 - \log_{0.1} 0.2

\log_{3} 9^{2.5} - \log_{4} 4^{0.5}

\log_{4} 16^{\frac{3}{2}} + \log_{3} 3^{\frac{1}{4}}

\log_{3} 7 + \log_{3} \frac{81}{7}

9000003802

Level:

In the following list identify a function with graph through the points

[5; 0]

and

[- 1; - 2]

y = \log_{2} (x + 3) - 3

y = \log_{5} (10 - x) - 1

y = \log_{3} (4 + x) - 2

y = 2 - \log_{3} (4 + x)

y = 3 - \log_{2} (x + 3)

y = 1 - \log_{5} (10 - x)

9100004907

Level:

Identify a possible graph of the function

f : y = \log_{0.2} x

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