9000003701
Level:
A
Identify a possible analytic expression for the exponential function graphed in the
picture.
\(y = 2^{x-1} - 2\)
\(y = 2^{x+1} - 2\)
\(y = 2^{x+1} + 2\)
\(y = 2^{x-1} + 2\)
Exponential Functions
9000003602
Level:
B
Which values of the real parameter
\(p\) ensure that
the function \(f(x) = \left (\frac{p+1}
{p-3}\right )^{x}\)
is an increasing function?
\(p\in (3;\infty )\)
\(p\in \mathbb{R}\)
\(p\in \mathbb{R}\setminus \{3\}\)
\(p\in (-\infty ;-1)\cup (3;\infty )\)
9000003603
Level:
B
What are the values of the real \( a \), that satisfy inequality \(\left (\sqrt{3} -\sqrt{2}\right )^{2a+1} > \left (\sqrt{3} -\sqrt{2}\right )^{4-a}\)?
\(a < 1\)
\(a > 0\)
\(0 < a < 1\)
\(a > 1\)
9000003702
Level:
A
In the following list identify a function whose graph passes through the points
\([3;0]\) and
\([5;3]\).
\(f(x) = \left (\frac{1}
{2}\right )^{3-x} - 1\)
\(f(x) = \left (\frac{1}
{2}\right )^{3-x} + 1\)
\(f(x) = 1 -\left (\frac{1}
{2}\right )^{x-3}\)
\(f(x) = \left (\frac{1}
{2}\right )^{x-3} + 1\)
\(f(x) = 1 -\left (\frac{1}
{2}\right )^{x+3}\)
\(f(x) = \left (\frac{1}
{2}\right )^{x-3} - 1\)
9000003703
Level:
A
In the following list identify a point which is not on the graph of the function
\(f(x) = 3 -\left (\frac{1}
{3}\right )^{x}\).
\(C = [-2;6]\)
\(A = [-1;0]\)
\(B = \left [1; \frac{8}
{3}\right ]\)
\(D = [0;2]\)
\(E = [-3;-24]\)
\(F = \left [2; \frac{26}
{9} \right ]\)
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 \(3\).
9100003606
Level:
A
Identify a possible graph of the following function.
\[
f(x) = \left (\frac{2}
{5}\right )^{x+2} - 1
\]
