Exponential functions

2010013021

Level: 
A
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 \(f(x)=\left(\frac15\right)^{x+1}-6\)?
\(\vec{u}=\left(-4;-2\right)\)
\(\vec{u}=\left(4;2\right)\)
\(\vec{u}=\left(4;-2\right)\)
\(\vec{u}=\left(-4;2\right)\)

2010013020

Level: 
A
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 \(f(x)=\left(\frac15\right)^{3-x}-4\)?
\(\vec{u}=\left(4;2\right)\)
\(\vec{u}=\left(-4;-2\right)\)
\(\vec{u}=\left(4;-2\right)\)
\(\vec{u}=\left(-4;2\right)\)

2010013019

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=\left(\frac14\right)^{5-x}-1\) be translated to get the graph of the function \(f(x)=4^{x-2}+3\)?
\(\vec{u}=\left(-3;4\right)\)
\(\vec{u}=\left(-3;-4\right)\)
\(\vec{u}=\left(3;4\right)\)
\(\vec{u}=\left(3;-4\right)\)

2010013018

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=\left(\frac14\right)^{x-2}+3\) be translated to get the graph of the function \(f(x)=4^{5-x}-1\)?
\(\vec{u}=\left(3;-4\right)\)
\(\vec{u}=\left(-3;-4\right)\)
\(\vec{u}=\left(3;4\right)\)
\(\vec{u}=\left(-3;4\right)\)

2010013017

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 \(y=2\) is false?
The graph of \(f\) and the line do not have a common point for any \(m\in\left(-\infty;2\right)\).
The graph of \(f\) and the line do not have a common point for any \(m\in\left. [ 2;\infty\right)\).
The graph of \(f\) and the line do not have a common point for \(m=2\).
The graph of \(f\) and the line do not have a common point for any \(m\in\left(2;\infty\right)\).

2010013016

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 \(y=-2\) is false?
The graph of \(f\) and the line do not have a common point for any \(m\in\left(2;\infty\right)\).
The graph of \(f\) and the line do not have a common point for any \(m\in\left(-\infty;2 \right. ] \).
The graph of \(f\) and the line do not have a common point for \(m=2\).
The graph of \(f\) and the line do not have a common point for any \(m\in\left(-\infty;2\right)\).

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 \(m\in\mathbb{R}\).

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 \(m\in\mathbb{R}\).