1103019002
Level:
A
One of the given graphs is a graph of an exponential function. Choose this graph.
Exponential functions
1003019001
Level:
A
Which of the following functions is not an exponential function?
\( f(x)=x^3 \)
\( g(x)= \mathrm{e}^{-3x} \)
\( h(x)= 5^{\frac x3} \)
\( i(x)= \left(\frac53\right)^x \)
1103024908
Level:
B
The graphs of functions \(f(x)=a\cdot 2^{bx}+2\), where \(a\in\{-1,1\}\), \(b\in\{-1,1\}\), are below. Identify which of the graphs represents the function that is increasing, bounded below, and has an asymptote at \(y=2\).
1003024907
Level:
B
Choose the correct list of properties of the function \( f(x)= -\left(\frac12\right)^{-x} \).
decreasing, bounded above, asymptote at \( y=0 \)
decreasing, bounded below, asymptote at \( x=0 \)
increasing, bounded below, asymptote at \( x=0 \)
increasing, bounded below, asymptote at \( y=0 \)
1103024906
Level:
B
The graph of function \(-3^{-x}\) is below. Choose the correct list of properties of \( f\).
increasing, bounded above, asymptote at \( y=0 \)
decreasing, bounded above, asymptote at \( y=0 \)
decreasing, bounded below, asymptote at \( x=0 \)
increasing, bounded below, asymptote at \( x=0 \)
1003024905
Level:
B
Which of the following functions is bounded above?
\( f(x) = -3^{-x} \)
\( f(x) = \left(\frac13\right)^{-x} \)
\( f(x) = 3^x \)
\( f(x) = \left(\frac13\right)^x \)
1003024904
Level:
B
Which of the following functions is decreasing?
\( f(x)=\left(\frac15\right)^x \)
\( f(x)=-5^{-x} \)
\( f(x)=\left(\frac15\right)^{-x} \)
\( f(x)=5^x \)
1003024903
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( 0 < b < 1 \), find the correct statement.
Function \( f \) is increasing.
Function \( f \) is decreasing.
Function \( f \) is nonincreasing.
Function \( f \) is nondecreasing.
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.
1003024901
Level:
B
Given the increasing exponential function \(f(x)=a^x\), choose the correct statement about the base \(a\).
\(a > 1\)
\(a=1\)
\(a < 1\)
\( 0 < a < 1 \)