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$5.2 Graphs of Reciprocal Functions (Adapted from Worksheet 5B, Workbook 3A, p. 92-95) 3. (a) Complete the table of values for y=x+(8)/(x)-9. (b) Plot the points and join them with a smooth curve. x 1 3 4 5 8 y 6 -3.3 -3 -24 0 (c) Use your graph to find the solutions of x+(8)/(x)=7. {:[x+(2)/(x)-9=7-9],[y=-2]:} Answer x= qquad 1.4 . x= 5. qquad (d) The equation (m-1)x^(2)+9x-8=0 has no solution in the interval 0.5 <= x <= 7. Suggest a value of m and draw the corresponding straight line on the same grid to show that the equation has no solution in the given interval. x^(2)+9x-8=-2$

$5$ . $2$ Graphs of Reciprocal Functions (Adapted from Worksheet $5$ B, Workbook $3$ A, p. $92$ $-95$ ) $\newline$ $3$ . (a) Complete the table of values for $y=x+\frac{8}{x}-9$ . $\newline$ (b) Plot the points and join them with a smooth curve. $\newline$ \begin{tabular}{|c|c|c|c|c|c|} $\newline$ \hline $x$ & $1$ & $3$ & $4$ & $5$ & $8$ \\ $\newline$ \hline $y$ & $6$ & $-3$ . $3$ & $-3$ & $-24$ & $0$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ (c) Use your graph to find the solutions of $x+\frac{8}{x}=7$ . $\newline$ $\begin{array}{c} x+\frac{2}{x}-9=7-9 \\ y=-2 \end{array}$ $\newline$ Answer $x=$ $\qquad$ $1$ . $4$ . $x=$ $5$ . $\qquad$ $\newline$ (d) The equation $(m-1) x^{2}+9 x-8=0$ has no solution in the interval $0.5 \leq x \leq 7$ . $\newline$ Suggest a value of $x$ $0$ and draw the corresponding straight line on the same grid to show that the equation has no solution in the given interval. $\newline$ $x^{2}+9 x-8=-2$

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Math Problems

Algebra 1

Write two-variable inequalities: word problems

Full solution

5

2

Graphs of Reciprocal Functions (Adapted from Worksheet

5

B, Workbook

3

A, p.

92

-95

)

\newline

3

. (a) Complete the table of values for

y=x+\frac{8}{x}-9

\newline

(b) Plot the points and join them with a smooth curve.

\newline

\begin{tabular}{|c|c|c|c|c|c|}

\newline

\hline

x

1

3

4

5

8

\newline

\hline

y

6

-3

3

-3

-24

0

\newline

\hline

\newline

\end{tabular}

\newline

x+\frac{8}{x}=7

\newline

\begin{array}{c} x+\frac{2}{x}-9=7-9 \\ y=-2 \end{array}

\newline

Answer

x=

\qquad

1

4

x=

5

\qquad

\newline

(d) The equation

(m-1) x^{2}+9 x-8=0

has no solution in the interval

0.5 \leq x \leq 7

\newline

Suggest a value of

x

0

and draw the corresponding straight line on the same grid to show that the equation has no solution in the given interval.

\newline

x^{2}+9 x-8=-2

Rearrange the equation: To find the values of $x$ when $x + \frac{8}{x} = 7$ , rearrange the equation to $x^2 - 7x + 8 = 0$ .
Factor the quadratic equation: Factor the quadratic equation to $(x - 1)(x - 8) = 0$ .
Set equal to zero: Set each factor equal to zero: $x - 1 = 0$ or $x - 8 = 0$ .
Solve for x: Solve for x: $x = 1$ or $x = 8$ .
Calculate the discriminant: For the equation $(m-1)x^2 + 9x - 8 = 0$ , to have no solution in the interval $0.5 \leq x \leq 7$ , the discriminant must be negative.
Simplify the discriminant: The discriminant is $b^2 - 4ac$ , where $a = m - 1$ , $b = 9$ , and $c = -8$ .
Set discriminant less than $0$ : Calculate the discriminant: $(9)^2 - 4(m - 1)(-8)$ .
Solve for $m$ : Simplify the discriminant: $81 + 32m - 32$ .
Choose a value for $m$ : Set the discriminant less than $0$ : $81 + 32m - 32 < 0$ .
Plot the line: Solve for $m$ : $32m < -49$ .
Plot the line: Solve for $m$ : $32m < -49$ .Divide by $32$ : $m < -\frac{49}{32}$ .
Plot the line: Solve for $m$ : $32m < -49$ . Divide by $32$ : $m < -\frac{49}{32}$ . Choose a value for $m$ that is less than $-\frac{49}{32}$ , for example, $m = -2$ .
Plot the line: Solve for $m$ : $32m < -49$ .Divide by $32$ : $m < -\frac{49}{32}$ .Choose a value for $m$ that is less than $-\frac{49}{32}$ , for example, $m = -2$ .Plot the line $y = (m-1)x^2 + 9x - 8$ on the same grid to show it has no solution in the interval $0.5 \leq x \leq 7$ .