A | math4u.vsb.cz

2010013013

Level:

Find the formula of an exponential function \(f(x)=a^x\), if you know that the point \(P=\left[-\frac12;7\right]\) lies on its graph.

\(f(x)=\left(\frac1{49}\right)^x\)

\(f(x)=\left(-\frac12\right)^x\)

\(f(x)=\left(\frac17\right)^x\)

\(f(x)=\left(-\frac17\right)^x\)

2010013012

Level:

Find the formula of an exponential function \(f(x)=a^x\), if you know that the point \(P=\left[-\frac12;8\right]\) lies on its graph.

\(f(x)=\left(\frac1{64}\right)^x\)

\(f(x)=\left(\frac12\right)^x\)

\(f(x)=\left(\frac18\right)^x\)

\(f(x)=\left(-\frac12\right)^x\)

2010013009

Level:

Given the function \(f(x)=2^x-3\), find the value of the function \(g(x)=f(x+1)-1\) for \(x=2\).

\(4\)

\(2\)

\(6\)

\(5\)

2010013008

Level:

Given the function \(f(x)=3^x+1\), find the value of the function \(g(x)=f(x+1)\) for \(x=2\).

\(28\)

\(16\)

\(25\)

\(10\)

2010013007

Level:

Find the range of the function \(f(x)=\left(\frac12\right)^{1-x}+2\).

\(\left(2;\infty\right)\)

\(\left(-2;\infty\right)\)

\(\left(-\infty;2\right)\)

\(\left(1;\infty\right)\)

2010013006

Level:

Find the range of a function \(f(x)=2^{1-x}-3\).

\(\left(-3;\infty\right)\)

\(\left(1;\infty\right)\)

\(\left(-\infty;-3\right)\)

\(\left(3;\infty\right)\)

2010013005

Level:

What value takes the function \(f(x)=8^x\) for the value of the argument \(x=-\frac23\)?

\(0.25\)

\(4\)

\(\frac1{2^3}\)

\(\frac1{\sqrt[3]{8}}\)

2010013004

Level:

What value takes the function \(f(x)=9^x\) for the value of the argument \(x=-\frac32\)?

\(\frac1{3^3}\)

\(27\)

\(\frac1{\sqrt[3]{81}}\)

\(\frac1{81}\)

2010017803

Level:

Determine the values of \( a \) and \( b \) (\( a \), \( b \in\mathbb{R} \)) such that the function \[ f(x)=ax^3-2bx+2 \] has a local extremum of \( 6 \) at \( x=-1 \).

\( a=2 \), \( b=3 \)

\( a=-2 \), \( b=3 \)

\( a=-2 \), \( b=-3 \)

\( a=2 \), \( b=-3 \)

The probability that an accident occurs in a cloudy day is two times greater than in a sunny day. There were \(20\) sunny days and \(10\) cloudy days in April. In this month exactly one accident happened. What is the probability that this accident occurred in a sunny day?

It is the same as in a cloudy day.

It is greater than in a cloudy day.

It is smaller than in a cloudy day.

It is \(\frac14\).

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