the following is an incomplete table of values for the graph of y = x²+1/x.\n|x|0.25|0.5|0.8|1|1.5|2|2.5|3|\n…

the following is an incomplete table of values for the graph of y = x²+1/x.\n|x|0.25|0.5|0.8|1|1.5|2|2.5|3|\n|y|4.1|2.3|1.9|p|2.9|4.5|q|9.3|\n(a) calculate the value of p and the value of q.\n(b) taking 4 cm to represent 1 unit on the x - axis and 2 cm to represent 1 unit on the y - axis, draw the graph of y = x²+1/x for 0.25≤x≤3.\n(c) on the same axes draw the graph of 2y = 5x + 2.

the following is an incomplete table of values for the graph of y = x²+1/x.\n|x|0.25|0.5|0.8|1|1.5|2|2.5|3|\n|y|4.1|2.3|1.9|p|2.9|4.5|q|9.3|\n(a) calculate the value of p and the value of q.\n(b) taking 4 cm to represent 1 unit on the x - axis and 2 cm to represent 1 unit on the y - axis, draw the graph of y = x²+1/x for 0.25≤x≤3.\n(c) on the same axes draw the graph of 2y = 5x + 2.

Answer

Explanation:

Step1: Calculate the value of (p)

Substitute (x = 1) into (y=x^{2}+\frac{1}{x}). [y=1^{2}+\frac{1}{1}=1 + 1=2]

Step2: Calculate the value of (q)

Substitute (x = 2.5) into (y=x^{2}+\frac{1}{x}). [y=(2.5)^{2}+\frac{1}{2.5}=6.25+0.4 = 6.65]

Answer:

(a) (p = 2), (q=6.65) (b) (Drawing the graph requires manual - work on graph - paper and cannot be fully represented in text. The general steps are: mark the (x) - values from (0.25) to (3) on the (x) - axis according to the scale (4\ cm) for (1) unit, mark the (y) - values from the table according to the scale (2\ cm) for (1) unit, and then plot the points ((x,y)) and connect them with a smooth curve.) (c) First, rewrite the equation (2y = 5x+2) as (y=\frac{5x + 2}{2}=2.5x + 1). Then, find some points on the line. For example, when (x = 0), (y=1); when (x = 1), (y=2.5\times1+1=3.5); when (x = 2), (y=2.5\times2+1=6). Plot these points on the same axes as the graph of (y=x^{2}+\frac{1}{x}) and draw a straight - line through them.