Exponential functions

9000003607

Level: 
C
The function \(f(x) = \left (\frac{1} {3}\right )^{x}\) is graphed in the picture. Identify a possible analytic expression for the function \(g\).
\(y = 3^{|x|}- 1\)
\(y = \left |\left (\frac{1} {3}\right )^{x} - 1\right |\)
\(y = \left (\frac{1} {3}\right )^{|x|}- 1\)
\(y = \left (\frac{1} {3}\right )^{|x-1|}\)
\(y = \left |3^{x} - 1\right |\)
\(y = 3^{|x-1|}\)

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 \(3\).

9000003702

Level: 
A
In the following list identify a function whose graph passes through the points \([3;0]\) and \([5;3]\).
\(f(x) = \left (\frac{1} {2}\right )^{3-x} - 1\)
\(f(x) = \left (\frac{1} {2}\right )^{3-x} + 1\)
\(f(x) = 1 -\left (\frac{1} {2}\right )^{x-3}\)
\(f(x) = \left (\frac{1} {2}\right )^{x-3} + 1\)
\(f(x) = 1 -\left (\frac{1} {2}\right )^{x+3}\)
\(f(x) = \left (\frac{1} {2}\right )^{x-3} - 1\)