1103019605
Level:
B
What are the values of the real variable \( x \), if \( 5^x \leq 1 \)? Use the graph of \( f(x)=5^x \) given below.
\( x\in (-\infty;0] \)
\( x\in [0;\infty) \)
\( x\in (-\infty;0) \)
\( x\in (0;\infty) \)
Exponential functions
1103019604
Level:
B
What are the values of the real variable \( x \), if \( 0.7^x \leq 1 \)? Use the graph of \( f(x)=0.7^x \) given below.
\( x\in[0;\infty) \)
\( x\in(-\infty;0) \)
\( x\in(-\infty;0] \)
\( x\in(0;\infty) \)
1103019603
Level:
B
Identify which of the relations between \( m \) and \( n \) ensures \( \left(\frac{12}7\right)^m < \left(\frac{12}7\right)^n \). Use the graph of \( f(x) = \left(\frac{12}7\right)^x \) given below.
\( m < n \)
\( m > n \)
\( m = n \)
\( m \geq n \)
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 \( 1 \).
\( 2 \)
\( 4 \)
\( 3 \)
\( 1 \)
1103019601
Level:
B
Consider values
\[ 0.7^{-0.5};\ \left(\frac58\right)^6;\ \left(\frac32\right)^{-5};\ 3.5^0;\ 0.4^4;\ 5^3\text{.} \]
Determine how many of the values are greater than \( 1 \). Use the graph of an exponential function given below.
\( 2 \)
\( 4 \)
\( 3 \)
\( 1 \)
1003025504
Level:
C
Find the range of the function \( f(x)=\Bigl|\left(\frac13\right)^x-1\Bigr|\).
\( [ 0;\infty) \)
\( ( 0;\infty) \)
\( (-1;\infty) \)
\( [ -1;\infty) \)
1003025503
Level:
C
Find the domain of the function \( f(x)=\sqrt{3^x}\).
\( (-\infty;\infty) \)
\( (0;\infty) \)
\( [0;\infty) \)
\( (-\infty;0) \)
1103025502
Level:
C
Identify a possible graph of the function \( f(x)=\Bigl|\left(\frac12\right)^x-1\Bigr|\).
1103025501
Level:
C
Identify a possible graph of the function \( f(x)= 2^{|x|}-1\).
1103019002
Level:
A
One of the given graphs is a graph of an exponential function. Choose this graph.
