1003162202
Level:
A
Let \( f(x)=x^{-3} \). Identify which of the following statements is true.
\( f\left(-\frac23\right)=-\frac{27}8 \)
\( f(0)=1 \)
\( f\left(-\frac1{10}\right)=-0.001 \)
\( f(0.2)=\frac1{125} \)
Power and radical functions
1003162201
Level:
A
Let \( f(x)=x^{-2} \). Identify which of the following statements is false.
\( f\left(\frac23\right)=\frac49 \)
\( f(-0.125)=64 \)
\( f\left(\frac14\right)=16 \)
\( f\left(\frac1{0.5}\right)=\frac14 \)
1003154402
Level:
A
Find the false statement about the function \( f(x)=3-(x+2)^4 \).
The function \( f \) is even.
The function \( f \) has the maximum at \( x=-2 \).
The function \( f \) is bounded above.
The range of the function \( f \) is the interval \( (-\infty; 3] \).
1003154401
Level:
A
Find the true statement about the function \( f(x)=2-(x-1)^3 \).
The function \( f \) is an injective (one-to-one) function.
The function \( f \) is increasing.
The function \( f \) is odd.
The function \( f \) has the maximum at \( x=1 \).
1103143503
Level:
A
The graphs represent the parts of the functions \( f(x)=x^4 \) and \( g(x)=x^6 \). Identify which of the following statements is true.
The solution set of the inequality \( x^4 \leq x^6 \) is \( (-\infty; -1]\cup[1;\infty)\cup\{0\} \).
The solution set of the inequality \( x^4 > x^6 \) is \( (-1;1) \).
The solution set of the equation \( x^6=x^4 \) is \( \{0;1\} \).
The solution set of the inequality \( x^6 \geq x^4 \) is \( (-\infty; -1]\cup[1; \infty) \).
1103143502
Level:
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^5 \). Identify which of the following inequalities has the solution set \( (-1;0)\cup(1;\infty) \).
\( x^3 < x^5 \)
\( x^5 \geq x^3 \)
\( x^3 > x^5 \)
\( x^3 > -1 \)
1103143501
Level:
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^4 \). Identify which of the following statements is false.
The solution set of the inequality \( x^4 > x^3 \) is \( (1;\infty) \).
The solution set of the inequality \( x^4 > 0 \) is \( (-\infty;0)\cup(0;\infty) \).
The solution set of the equation \( x^3 = x^4 \) is \( \{0;1\} \).
The solution set of the inequality \( x^3 \geq x^4 \) is \( [0;1] \).
1103143403
Level:
A
The graphs represent the parts of the functions \( f(x)=x^3 ;\ g(x)=x^4;\ h(x)=x^5 \). Identify which of the following statements is false.
\( \left(-\frac13\right)^5 < \left(-\frac13\right)^3 \)
\( \left(\frac12\right)^5 < \left(-\frac12\right)^4 \)
\( (-3)^4 > (3)^3 \)
\( \left(\frac14\right)^3 \geq (-0.25)^4 \)
1103143402
Level:
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^4 \). Identify which of the following statements is true.
\( (-3)^4 > (2)^4 \)
\( (-2)^4 < \left(-\frac12\right)^4 \)
\( \left(-\frac14\right)^4 \geq (0.3)^4 \)
\( (-1)^4 < (1)^4 \)
1103143401
Level:
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^4 \). Identify which of the following statements is false.
\( \left(-\frac12\right)^3 > (2)^3 \)
\( (-2)^3 < \left(-\frac12\right)^3 \)
\( \left(\frac13\right)^3 \geq (0.3)^3 \)
\( (-1)^3 \leq (1)^3 \)