Question

Please refer to the picture ​

Answer 1

The graph is shown in the attachment below

From the graph, the solution to the equation $\frac{4}{x}-2x+1=0$ is x = -1.2 and x = 1.7

From the picture, we are to draw the graph of the function

$y = -\frac{4}{x}$ for the range of values $-3\leq x\leq 3$ (that is for values of x from -3 to 3)

First we will create the table of values for the function

Table of values for the function $y = -\frac{4}{x}$

x y

-3 1.33

-2 2

-1 4

0 Undefined

1 -4

2 -2

3 -1.33

(Shown better in the docx attachment)

The graph for the function $y = -\frac{4}{x}$  (purple lines) is also shown in the attachment.

To use the graph to solve the equation $\frac{4}{x}-2x+1=0$

We will rewrite the equation so that it takes the form $y = -\frac{4}{x}$

From $\frac{4}{x}-2x+1=0$

Then, $-2x+1= -\frac{4}{x}$

∴ $y = -2x+1$

Hence, we will plot the graph for the function $y = -2x+1$ on the same graph and the points of intersection gives the solution.

The function is a linear equation

The points of intersection on the x and y axes (x-intercept and y-intercept) are enough to plot a straight line graph as shown in the table below as well as in the graph

x y

0 1

0.5 0

(Shown better in the docx attachment)

The straight red lines in the graph shows the plot for the function $y = -2x+1$

From the graph, the points of intersection are -1.2 and 1.7

Hence, the solution to the equation $\frac{4}{x}-2x+1=0$ is x= -1.2 and x = 1.7

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