Het begrip functie

Antwoorden bij de opgaven

1. 1. A
   2. 11,232
   3. van 0 tot en 175,5 kW
   4. ongeveer 17,9 m/s
2. 1. ${\displaystyle P\left(v\right)=\mathrm{0,208}{v}^3}$
   2. 208
   3. 0 ≤ X ≤ 20 en 0 ≤ Y ≤ 1664
   4. ongeveer 5,78 m/s is ongeveer 20,8 km/h
3. 1. ${\displaystyle x=2}$ geeft ${\displaystyle y=\pm \sqrt{96}}$
   2. ${\displaystyle y=\pm \sqrt{100-x^2}}$
   3. ${\displaystyle y_1\left(x\right)=\sqrt{100-x^2}}$ en ${\displaystyle y_2\left(x\right)=-\sqrt{100-x^2}}$
   4. standaardinstelling kan
   5. ${\displaystyle y_1\left(5\right)=\sqrt{75}}$ en ${\displaystyle y_2\left(5\right)=-\sqrt{75}}$
4. C en D
5. 1. ${\displaystyle x=0}$ V ${\displaystyle x=4}$
   2. (0,0) en (4,0)
   3. ${\displaystyle x=-1}$ V ${\displaystyle x=5}$
6. 1. ${\displaystyle T=\mathrm{0,44}}$
   2. Ja, bij elk gewicht hoort precies één tarief (boven 250 g is het geen brief).
   3. Nee, je weet alleen in welke gewichtscategorie de brief zit.
   4. 50 ≤ ${\displaystyle G}$ < 100
   5. Nee, bij elke waarde van ${\displaystyle T}$ horen meerdere waarden van ${\displaystyle G}$.
7. A, C en D
8. 1. -
   2. ${\displaystyle \left(\sqrt{130}\mathrm{,0}\right)}$ en ${\displaystyle (-\sqrt{130}\mathrm{,0})}$ met top ${\displaystyle (0,-130)}$
   3. bijvoorbeeld –15 ≤ X ≤ 15 en –130 ≤ Y ≤ 130
   4. twee snijpunten
   5. ${\displaystyle (-10,-30)}$ en ${\displaystyle \left(\mathrm{13,39}\right)}$
9. 1. van ${\displaystyle y_1}$: ${\displaystyle (\pm \mathrm{3,0})}$ en ${\displaystyle (\pm \mathrm{2,0})}$
      van ${\displaystyle y_2}$: ${\displaystyle (-\mathrm{3,0})}$ en ${\displaystyle \left(\mathrm{2,0}\right)}$
   2. -
   3. ${\displaystyle (-\mathrm{3,0})}$, ${\displaystyle (-\mathrm{1,79};\mathrm{4,58})}$, ${\displaystyle \left(\mathrm{2,0}\right)}$ en ${\displaystyle (\mathrm{2,79};-\mathrm{4,58})}$
10. 1. ${\displaystyle f\left(3\right)=23}$
    2. ${\displaystyle f\left(x\right)=8}$ geeft ${\displaystyle x=0}$ V ${\displaystyle x=\pm 2}$
    3. -
    4. Ja
    5. Nee, bijvoorbeeld bij b heb je een tegenvoorbeeld.
11. 1. Bij elke waarde van ${\displaystyle a}$ hoort precies één waarde van ${\displaystyle K}$.
    2. ${\displaystyle K\left(100\right)=67}$
    3. ${\displaystyle K\left(a\right)=42+\mathrm{0,25}a}$
    4. 1832 m³
12. 1. ${\displaystyle (\pm \mathrm{10,0})}$ en top ${\displaystyle \left(\mathrm{0,100}\right)}$
    2. -
    3. ${\displaystyle (-\mathrm{7,07};50)}$ en ${\displaystyle (\mathrm{7,07};50)}$
13. 1. van ${\displaystyle y_1}$: ${\displaystyle \left(\mathrm{0,0}\right)}$ en ${\displaystyle (\pm \mathrm{2,0})}$
       van ${\displaystyle y_2}$: ${\displaystyle \left(\mathrm{0,0}\right)}$ en ${\displaystyle \left(\mathrm{4,0}\right)}$
    2. -
    3. ${\displaystyle \left(\mathrm{0,0}\right)}$ en ${\displaystyle (\mathrm{2,3};\mathrm{3,9})}$
14. 1. ${\displaystyle \left(\mathrm{0,0}\right)}$ en ${\displaystyle \left(\mathrm{100,0}\right)}$
    2. ${\displaystyle \left(\mathrm{0,0}\right)}$ en ${\displaystyle (\pm \mathrm{10,0})}$
    3. ${\displaystyle (-\mathrm{30,0})}$ en ${\displaystyle \left(\mathrm{50,0}\right)}$ met top ${\displaystyle (10,-1600)}$
    4. ${\displaystyle (-\mathrm{125,0})}$
15. 1. ${\displaystyle V=2\pi r^3}$
    2. -
    3. ${\displaystyle r\approx \mathrm{5,42}}$
16. 1. A en B
    2. B en C
17. 1. ${\displaystyle f\left(5\right)=250}$ en ${\displaystyle f(-5)=-2250}$
    2. ${\displaystyle x=0}$ V ${\displaystyle x=10}$
    3. ${\displaystyle \left(\mathrm{0,0}\right)}$, ${\displaystyle \left(\mathrm{8,64}\right)}$ en ${\displaystyle \left(\mathrm{12,96}\right)}$