9100003606
Level:
A
Identify a possible graph of the following function.
\[
f(x) = \left (\frac{2}
{5}\right )^{x+2} - 1
\]
Exponential functions
1003019602
Level:
B
Consider values
\[ 4^5;\ 0.2^{\frac12};\ \left(\frac54\right)^0;\ \left(\frac13\right)^{-3};\ \left(\frac76\right)^{-3};\ 2.5^{0.6}\text{.} \]
Without using a calculator, determine how many of the values are less than \( 1 \).
\( 2 \)
\( 4 \)
\( 3 \)
\( 1 \)
1003019607
Level:
B
Which of the relations between \( m \) and \( n \) ensures \( \left(\frac45\right)^m < \left(\frac45\right)^n \)?
\( m > n \)
\( m \geq n \)
\( m = n \)
\( m < n \)
1003019608
Level:
B
Which of the relations between \( m \) and \( n \) ensures \( \left(\frac54\right)^m < \left(\frac54\right)^n \)?
\( m < n \)
\( m \geq n \)
\( m = n \)
\( m > n \)
1003019609
Level:
B
What are the values of the real \( a \), that satisfy inequality \( a^{\frac25} > a^{\frac45}\)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)
1003019610
Level:
B
What are the values of the real \( a \), that satisfy inequality \( a^{-3} > a^{-2}\)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)
1003019611
Level:
B
Identify which of the following relations is correct.
\( \left(\frac15\right)^{-6} > \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^2 > \left(\frac15\right)^7 \)
\( \left(\frac15\right)^7 > \left(\frac15\right)^2 > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^{-\frac25} > \left(\frac15\right)^{-6} \)
\( \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{-6} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^2 > \left(\frac15\right)^7 \)
\( \left(\frac15\right)^{-6} > \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^7 > \left(\frac15\right)^2 \)
1003019612
Level:
B
Identify which of the following relations is correct.
\( 2^7 > 2^2 > 2^{\frac25} > 2^{-\frac25} > 2^{-6} \)
\( 2^{-6} > 2^{-\frac23} > 2^{\frac25} > 2^2 > 2^7 \)
\( 2^{-\frac23} > 2^{-6} > 2^{\frac25} > 2^2 > 2^7 \)
\( 2^{-6} > 2^{-\frac23} > 2^{\frac25} > 2^7 > 2^2 \)
1003024901
Level:
B
Given the increasing exponential function \(f(x)=a^x\), choose the correct statement about the base \(a\).
\(a > 1\)
\(a=1\)
\(a < 1\)
\( 0 < a < 1 \)
1003024902
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( b > 0 \), find the correct statement.
Function \( f \) is bounded above.
Function \( f \) is bounded below.
Function \( f \) is bounded.
Function \( f \) is unbounded.