C

9000007201

Level: 
C
Consider the function \[ f(x) = [x + 2] \] defined on the domain \(\mathop{\mathrm{Dom}}(f) = (1;2)\). Find the parameters \(a\) and \(b\) in the linear function \[ g(x) = ax + b \] which ensure that the functions \(f\) and \(g\) are identical on the domain of \(f\). \[ \] Hint: The function \(y = [x]\) is a floor function: the largest integer less than or equal to \(x\). For positive \(x\) it is also called the integer part of \(x\).
\(a = 0\), \(b = 3\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 3\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 0\), \(b = 4\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = -3\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)

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 \(g\).
\(y = 3^{|x|}- 1\)
\(y = \left |\left (\frac{1} {3}\right )^{x} - 1\right |\)
\(y = \left (\frac{1} {3}\right )^{|x|}- 1\)
\(y = \left (\frac{1} {3}\right )^{|x-1|}\)
\(y = \left |3^{x} - 1\right |\)
\(y = 3^{|x-1|}\)

9000003709

Level: 
C
Solve the following inequality. \[ \left (\frac{2} {3}\right )^{2-3x} < \frac{2^{x+1}} {3^{x+1}} \]
\(\left (-\infty ; \frac{1} {4}\right )\)
\(\left (-\frac{1} {4};\infty \right )\)
\((-\infty ;4)\)
\(\left (\frac{1} {4};\infty \right )\)
\((4;\infty )\)
\(\left (-\infty ;-\frac{1} {4}\right )\)