Zad. 1
[tex]f(x)=-2\frac12x-7\\f(-4)=-2\frac12*(-4)-7\\f(-4)=-\frac52*(-4)-7\\f(-4)=-5*(-2)-7\\f(=4)=10-7\\f(-4)=3[/tex]
Zad. 2
[tex]f(x)=3x-5\\3x-5=0 /+5\\3x=5 /:3\\x=\frac53[/tex]
Zad. 3
[tex]D \to x\in(-5; 6 > \\Zw \to y\in < -2; 4)\\\\\\[/tex]
[tex]\left \{ {{4=-5a+b /*(-3)} \atop {-2=-3a+b /*5}} \right. \\\left \{ {{-12=15a-3b} \atop {-10=-15a+5b}} \right. \\-12-10=-3b+5b\\-22=2b /:2\\-11=b\\-2=-3a-11 /+11\\9=-3a /:(-3)\\-3=a\\y=-3x-11\\-3x-11=0 /+11\\-3x=11 /:(-3)\\x=-\frac{11}3=-3\frac23\\[/tex]
[tex]\left \{ {{-2=-1a+b /*3} \atop {3=3a+b}} \right. \\\left \{ {{-6=-3a+3b} \atop {3=3a+b}} \right. \\-6+3=3b+b\\-3=4b /:4\\-\frac34=b\\-2=-a-\frac34 /*4\\-8=-4a-3 /+3\\-5=-4a /:(-4)\\\frac54=a\\y=\frac54x-\frac34\\\frac54x-\frac34=0 /*4\\5x-3=0\\5x=3 /:5\\x=\frac35[/tex]
[tex]\left \{ {{3=3a+b /*(-2)} \atop {-1=6a+b}} \right. \\\left \{ {{-6=-6a-2b} \atop {-1=6a+b}} \right. \\-6-1=-2b+b\\-7=-b\\b=7\\\\-1=6a+7 /-7\\-8=6a /:6\\a=-\frac86=-\frac43\\\\y=-\frac43x+7\\\\-\frac43x+7=0 /-7\\-\frac43x=-7 /*(-\frac34)\\x=\frac{21}4=5\frac14[/tex]
Miejsca zerowe:
[tex]x=-3\frac23 \text{ v } x=\frac35 \text{ v } x=5\frac14[/tex]
Przedzialy monotonicznosci:
f↓ dla x∈(-5; -3>∪<3; 6>
f↑ dla x∈<-1; 3>
f→ dla x∈<-3; -1>
Zad. 4
Przeksztalcenia wykresow funkcji w zalaczniku.
