Chapter 5.5, Problem 51PPE

To determine

Todetermine:The similarity and difference of the functions one represented by a graph and other by a table.

Answer to Problem 51PPE

The similarity and difference of the functions one represented by a graph and other by a table are:

Similarity: The curve represented by both the functions is a straight line, and both make y-intercepts $\left(0,3\right)$

Difference: The function represented by the graph is $y=3-\frac{3}{4}x$ and that by the table is $y=3-\frac{1}{2}x$ . The line represented by graph makes x-intercept $\left(4,0\right)$ and that represented by table is $\left(6,0\right)$ .

Explanation of Solution

Given information:

The graph of function and the table is given in Figure-1(a) and Figure-1(b) respectively.

  

Formulaused:

The equation of straight line passing that makes intercepts of lengths a and b on x-axis and y-axis respectively is given by $\frac{x}{a}+\frac{y}{b}=1$ .

Calculations:

Let $y=f\left(x\right)$ be a function represented by the graph (Figure-1(a)).

The straight line makes intercepts of lengths 4 units and 3 units on x-axis and y-axis respectively. Then equation of line is $\frac{x}{4}+\frac{y}{3}=1$ ,

  $\Rightarrow 3x+4y=12$

  $\Rightarrow y=\frac{12-3x}{4}$

  $\Rightarrow y=3-\frac{3}{4}x$

  $\Rightarrow f\left(x\right)=3-\frac{3}{4}x$

Thus, the function represented by the graph is $f\left(x\right)=3-\frac{3}{4}x$ .

Let $g\left(x\right)$ be a function represented by the graph (Figure-1(b)). The graph represented by table is shown in Figure-2 here.

  

The curve represented by the data of the table is a straight line that makes x-intercept and y-intercept of length 6 units and 3 units. Therefore, its equation is

Then equation of line is $\frac{x}{6}+\frac{y}{3}=1$ ,

  $\Rightarrow x+2y=6$

  $\Rightarrow y=\frac{6-x}{2}$

  $\Rightarrow y=3-\frac{1}{2}x$

  $\Rightarrow g\left(x\right)=3-\frac{1}{2}x$

Thus, the function represented by the table is $g\left(x\right)=3-\frac{1}{2}x$ .

The similarity and the difference in functions represented by graph (Figure-1 (a)) and the given table are:

Similarity: The curve represented by both the functions is a straight line, and both make y-intercepts $\left(0,3\right)$

Difference: The function represented by the graph is $y=3-\frac{3}{4}x$ and that by the table is $y=3-\frac{1}{2}x$ . The line represented by graph makes x-intercept $\left(4,0\right)$ and that represented by table is $\left(6,0\right)$ .