1103024908
Level:
B
The graphs of functions \(f(x)=a\cdot 2^{bx}+2\), 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 \(y=2\).
Exponential functions
2010010201
Level:
B
Which values of the real parameter
\(p\) ensure that
the function \(f(x) = \left (\frac{p-2}
{p+5}\right )^{x}\)
is an increasing function?
\(p\in (-\infty;-5 )\)
\(p\in \mathbb{R}\)
\(p\in (-\infty ;-5)\cup (2;\infty )\)
\(p\in (-5;-2 )\)
2010010202
Level:
B
Using properties of exponential function convert the
following inequality to an explicit inequality for the parameter
\(a\).
\[
\left (\sqrt{5} -\sqrt{3}\right )^{a+2} > \left (\sqrt{5} -\sqrt{3}\right )^{4a-1}
\]
\(a > 1\)
\(a < 1\)
\(a > 0\)
\(0 < a < 1\)
2010013001
Level:
B
Consider values
\[ 0.7^{-0.5};\ \left(\frac58\right)^6;\ \left(\frac32\right)^{-5};\ 3.5^{0};\ 0.4^4;\ 5^3\text{.} \]
Without using a calculator, determine how many of the values are greater than \( 1 \).
\( 2 \)
\( 4 \)
\( 3 \)
\( 1 \)
2010013002
Level:
B
For what values of the parameter \(a\) is the exponential function \(f(x)=(2a+3)^x\) increasing?
\(a>-1\)
\(a>-1.5\)
\(a< -1\)
\(-1.5< a< -1\)
2010013003
Level:
B
For what values of the parameter \(a\) is the exponential function \(f(x)=(2a+1)^x\) decreasing?
\(-0.5< a< 0\)
\(-1.5< a< 1\)
\(a< -1\)
\(a>-0.5\)
2010013010
Level:
B
Given the functions \(f(x)=2^{x+2}-3\) and \(g(x)=\left(\frac12\right)^x-3\), specify the quadrant of the coordinate system to which the point of intersecion of their graphs belongs.
\(III\)
\(IV\)
\(I\)
\(II\)
2010013011
Level:
B
Given the functions \(f(x)=3^{x-5}-2\) and \(g(x)=\left(\frac13\right)^{x+1}-2\), specify the quadrant of the coordinate system to which the point of intersection of their graphs belongs.
\(IV\)
\(III\)
\(II\)
\(I\)
2010013014
Level:
B
Let \(f\) be a function defined by \(f(x)=\left(\frac12\right)^{x-m}-m\), 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 \(m\in\left(-3;\infty\right)\).
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 \(m\in\left(-\infty;-3\right)\).
The graph of \(f\) and the line have always a common point for all \(m\in\mathbb{R}\).
2010013015
Level:
B
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 \(m\in\left(-\infty;-3\right)\).
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 \(m\in\left(-3;+\infty\right)\).
The graph of \(f\) and the line have always a common point for all \(m\in\mathbb{R}\).