Exponential functions

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 \(m\in\left(-\infty;2\right)\).

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 \(m\in\left(2;\infty\right)\).

9000003704

Level: 
B
The function \(g(x) = 3 - 3^{x}\) is graphed in the picture. In the following list identify one statement which is not true.
The range of the function \(g\) is \((-\infty ;3] \).
The function \(g\) is neither odd nor even.
The function \(g\) is decreasing on the domain.
The domain of the function \(g\) is \((-\infty ;\infty )\).
The function \(g\) is not bounded. It is bounded above.
All the values of the function \(g\) are smaller than \(3\).