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$Найдите значения функции в заданных точках x_(1),x_(2),x_(3) : а) y=3|x-1|+2x-5,x_(1)=-2,x_(2)=1,x_(3)=4; б) y=3|x+2|-2|x-1|,x_(1)=-2,x_(2)=0,x_(3)=1; в) y=(4x-8)/(x-2)+(2x+6)/(x+3),x_(1)=-3,x_(2)=1,x_(3)=2; г) y=(5-4x)/(2x+3)+1,x_(1)=-2,x_(2)=-1,5,x_(3)=1; д) y={[2x-1","" если "x <= 1","],[x^(2)","" если "1 < x < 2","x_(1)=-2","x_(2)=1","5","x_(3)=4;],[8-x^(2)","" если "x >= 2","]:} е) y={[(1)/(x)","" если "x < 1","],[x^(2)+3","" если "x >= 1","]quadx_(1)=-1,x_(2)=1,x_(3)=3:}.$

$93$ . Найдите значения функции в заданных точках $x_{1}, x_{2}, x_{3}$ : $\newline$ а) $y=3|x-1|+2 x-5, x_{1}=-2, x_{2}=1, x_{3}=4$ ; $\newline$ б) $y=3|x+2|-2|x-1|, x_{1}=-2, x_{2}=0, x_{3}=1$ ; $\newline$ в) $y=\frac{4 x-8}{x-2}+\frac{2 x+6}{x+3}, x_{1}=-3, x_{2}=1, x_{3}=2$ ; $\newline$ г) $y=\frac{5-4 x}{2 x+3}+1, x_{1}=-2, x_{2}=-1,5, x_{3}=1$ ; $\newline$ д) $y=\left\{\begin{array}{l}2 x-1, \text { если } x \leq 1, \\ x^{2}, \text { если } 1<x<2, x_{1}=-2, x_{2}=1,5, x_{3}=4 ; \\ 8-x^{2}, \text { если } x \geq 2,\end{array}\right.$ $\newline$ е) $y=\left\{\begin{array}{l}\frac{1}{x}, \text { если } x<1, \\ x^{2}+3, \text { если } x \geq 1,\end{array} \quad x_{1}=-1, x_{2}=1, x_{3}=3\right.$ .

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Math Problems

Grade 6

Integer inequalities with absolute values

Full solution

93

. Найдите значения функции в заданных точках

x_{1}, x_{2}, x_{3}

\newline

а)

y=3|x-1|+2 x-5, x_{1}=-2, x_{2}=1, x_{3}=4

;

\newline

б)

y=3|x+2|-2|x-1|, x_{1}=-2, x_{2}=0, x_{3}=1

;

\newline

в)

y=\frac{4 x-8}{x-2}+\frac{2 x+6}{x+3}, x_{1}=-3, x_{2}=1, x_{3}=2

;

\newline

г)

y=\frac{5-4 x}{2 x+3}+1, x_{1}=-2, x_{2}=-1,5, x_{3}=1

;

\newline

д)

y=\left\{\begin{array}{l}2 x-1, \text { если } x \leq 1, \\ x^{2}, \text { если } 1<x<2, x_{1}=-2, x_{2}=1,5, x_{3}=4 ; \\ 8-x^{2}, \text { если } x \geq 2,\end{array}\right.

\newline

е)

y=\left\{\begin{array}{l}\frac{1}{x}, \text { если } x<1, \\ x^{2}+3, \text { если } x \geq 1,\end{array} \quad x_{1}=-1, x_{2}=1, x_{3}=3\right.

Calculate $y$ for $x_1$ : Part (а): Calculate $y$ for $x_1 = -2$ using $y = 3|x-1| + 2x - 5$ . $\newline$ Calculation: $y = 3|-2-1| + 2(-2) - 5 = 3\times3 - 4 - 5 = 9 - 4 - 5 = 0$ .
Calculate $y$ for $x_2$ : Part (а): Calculate $y$ for $x_2 = 1$ using $y = 3|x-1| + 2x - 5$ . $\newline$ Calculation: $y = 3|1-1| + 2\times 1 - 5 = 3\times 0 + 2 - 5 = 0 + 2 - 5 = -3$ .
Calculate $y$ for $x_3$ : Part (а): Calculate $y$ for $x_3 = 4$ using $y = 3|x-1| + 2x - 5$ . $\newline$ Calculation: $y = 3|4-1| + 2\times 4 - 5 = 3\times 3 + 8 - 5 = 9 + 8 - 5 = 12$ .
Calculate $y$ for $x_1$ : Part (б): Calculate $y$ for $x_1 = -2$ using $y = 3|x+2| - 2|x-1|$ . $\newline$ Calculation: $y = 3|-2+2| - 2|-2-1| = 3\times 0 - 2\times 3 = 0 - 6 = -6$ .
Calculate y for $x_2$ : Part (б): Calculate y for $x_2 = 0$ using $y = 3|x+2| - 2|x-1|$ . Calculation: $y = 3|0+2| - 2|0-1| = 3\times 2 - 2\times 1 = 6 - 2 = 4$ .
Calculate $y$ for $x_3$ : Part (б): Calculate $y$ for $x_3 = 1$ using $y = 3|x+2| - 2|x-1|$ . $\newline$ Calculation: $y = 3|1+2| - 2|1-1| = 3\times3 - 2\times0 = 9 - 0 = 9$ .
Calculate $y$ for $x_1$ : Part (в): Calculate $y$ for $x_1 = -3$ using $y = \frac{4x-8}{x-2} + \frac{2x+6}{x+3}$ . $\newline$ Calculation: $y = \frac{4(-3)-8}{-3-2} + \frac{2(-3)+6}{-3+3} = \frac{-12-8}{-5} + \frac{-6+6}{0}$ . $\newline$ Error: Division by zero encountered.