Logarithmic functions | math4u.vsb.cz

1003136502

Level:

B

Consider the values \(\ \log_74;\) \(\log_{\frac47}{0.4};\) \(\log_40.7;\) \(\log_{\frac74}⁡4;\) \(\log_{0.7}⁡0.4;\) \(\log_{0.4}4;\) \(\log_7⁡{0.7}.\ \) Without using a calculator, determine how many of the given values are positive.

\( 4 \)

\( 3 \)

\( 2 \)

\( 5 \)

1103136501

Level:

B

Consider the values \( \log_{0.2}⁡3;\) \(\log_20.3;\) \(\log_{0.3}⁡1;\) \(\log_2⁡3;\) \(\log_{\frac32}⁡\frac23;\) \(\log_{\frac23}⁡2;\) \(\log_{0.3}\frac32.\) Determine how many of the given values are negative. Use the graph of a logarithmic function given below.

\( 5 \)

\( 4 \)

\( 3 \)

\( 2 \)

1103118505

Level:

B

Suppose a logarithmic function \( f \) is unbounded, increasing and \( f \) has an asymptote at \( x=-2 \). Given properties of \( f \), identify a possible graph of this function.

1103118504

Level:

B

Given the next graph of a logarithmic function \( f \), choose the correct list of properties of \( f \).

decreasing, asymptote at \( x=0 \), unbounded

decreasing, asymptote at \( y=0 \), unbounded

decreasing, asymptote at \( x=0 \), bounded below

increasing, asymptote at \( y=0 \), bounded below

1003118503

Level:

B

Which of the following functions is increasing?

\( f\colon y=-\log_{\frac12}x \)

\( f\colon y=-\log_2x \)

\( f\colon y=-2\log_2x \)

\( f\colon y=\log_{\frac12}x \)

1003118502

Level:

B

Given a function \( f(x)=b\cdot \log_a⁡x \), where \( a > 1 \) and \( b < 0 \), find the correct statement.

Function \( f \) is decreasing.

Function \( f \) is increasing.

Function \( f \) is bounded.

Function \( f \) is bounded below.

1003118501

Level:

B

Given a decreasing logarithmic function \( f(x)=\log_a⁡x \), choose the correct statement about the base \( a \).

\( 0 < a < 1 \)

\( a > 1 \)

\( a=1 \)

\( a < 1 \)

1103099811

Level:

A

Which of the following graphs is the graph of the function \( f(x)=2\log_2⁡x \)?

1103099810

Level:

A

Which of the following graphs is the graph of the function \( f(x)=2-\log_{0.4}⁡x \)?

1103099809

Level:

A

Below, we are given the graph of the logarithmic function \( f(x)=\log_4⁡(x-3) \). Use the graph of \( f \) as help to identify which of the next four given graphs is the graph of \( g(x)=\log_4⁡(3-x) \).