2010013002
Level:
B
For what values of the parameter \(a\) is the exponential function \(f(x)=(2a+3)^x\) increasing?
\(a>-1\)
\(a>-1.5\)
\(a< -1\)
\(-1.5< a< -1\)
Exponential functions
2010013001
Level:
B
Consider values
\[ 0.7^{-0.5};\ \left(\frac58\right)^6;\ \left(\frac32\right)^{-5};\ 3.5^{0};\ 0.4^4;\ 5^3\text{.} \]
Without using a calculator, determine how many of the values are greater than \( 1 \).
\( 2 \)
\( 4 \)
\( 3 \)
\( 1 \)
2110010205
Level:
A
Which of the given graphs is the graph of the function \( f(x)=5\cdot 0.2^{-x}\)?
2010010204
Level:
A
In the following list identify a point which is not on the graph of the function
\(f(x) = 4 -\left (\frac{1}
{2}\right )^{x}\).
\(A = [-2;8]\)
\(B =\left [1;\frac72\right]\)
\(C =\left [-1;2\right]\)
\(D =\left [0;3\right]\)
\(E =\left [-3;-4\right]\)
\(F =\left [2;\frac{15}4\right]\)
2010010203
Level:
A
In the following list identify a function whose graph passes through the points
\([2;6]\) and
\([4;14]\).
\(f(x) = \left (\frac{1}
{3}\right )^{2-x} +5\)
\(f(x) = \left (\frac{1}
{3}\right )^{2-x} -5\)
\(f(x) = \left (\frac{1}
{3}\right )^{x-2} -5\)
\(f(x) = 5-\left (\frac{1}
{3}\right )^{x-2} \)
\( f(x)=5+\left(\frac13\right)^{x-2}\)
\( f(x)=5-\left(\frac13\right)^{2-x}\)
2010010202
Level:
B
Using properties of exponential function convert the
following inequality to an explicit inequality for the parameter
\(a\).
\[
\left (\sqrt{5} -\sqrt{3}\right )^{a+2} > \left (\sqrt{5} -\sqrt{3}\right )^{4a-1}
\]
\(a > 1\)
\(a < 1\)
\(a > 0\)
\(0 < a < 1\)
2010010201
Level:
B
Which values of the real parameter
\(p\) ensure that
the function \(f(x) = \left (\frac{p-2}
{p+5}\right )^{x}\)
is an increasing function?
\(p\in (-\infty;-5 )\)
\(p\in \mathbb{R}\)
\(p\in (-\infty ;-5)\cup (2;\infty )\)
\(p\in (-5;-2 )\)
Transformations of Graphs of Exponential Functions
Submitted by ladislav.foltyn on Sat, 02/16/2019 - 12:03Exponential Inequalities -- Same Base
Submitted by ladislav.foltyn on Fri, 02/15/2019 - 13:46Question:
In the table, indicate for which values of the real parameter \( a \) the given inequality is satisfied.
1003101102
Level:
C
Find the false statement about the function \( f(x)=\left(\frac12\right)^{|x|} \).
The function \( f \) has the minimum at \( x=0 \).
The function \( f \) has the maximum at \( x=0 \).
The function \( f \) is bounded.
The function \( f \) is even.