Chapter 6.3, Problem 44SR

a.

To determine

Tabular : Express each statement using an inequality involving absolute value. Do not solve. Copy and complete the table .Substitute the x and $f(x)$ values for each point into each inequality. Mark whether the resulting statement is true or false.

Answer to Problem 44SR

Point	$f(x)\ge x-1.$	True/false	$f(x)\le x-1.$	True/false
(-4,2)	$2\ge -4-1$	true	$2\le -4-1$	false
(-2,2)	$2\ge -2-1$	true	$2\le -2-1$	false
(0.2)	$2\ge -0-1$	true	$2\le 0-1$	false
(2,2)	$2\ge 2-1$	true	$2\le 2-1$	false
(4,2)	$2\ge 4-1$	false	$2\le 3-1$	true

Explanation of Solution

Given: Given table is given below.

  

Calculation:

Fill in the table by substituting each point into the given inequalities determining if the inequalities are true or false.

Point	$f(x)\ge x-1.$	True/false	$f(x)\le x-1.$	True/false
(-4,2)	$2\ge -4-1$	true	$2\le -4-1$	false
(-2,2)	$2\ge -2-1$	true	$2\le -2-1$	false
(0.2)	$2\ge -0-1$	true	$2\le 0-1$	false
(2,2)	$2\ge 2-1$	true	$2\le 2-1$	false
(4,2)	$2\ge 4-1$	false	$2\le 3-1$	true

b.

To determine

You will investigate the graphs of linear inequalities on a coordinate plane.

Graphical : Graph $f(x)\ge x-1.$

Answer to Problem 44SR

  

Explanation of Solution

Given: Graph $f(x)\ge x-1.$

Calculation:

  $f(x)=x-1$ has a slope of 1 and a y-intercept of -1 so plot a point at -1 on the y-axis .Then go up 1 right 1 and plot a second point .Continue going up 1right 1 to plot additional points.

  

Conclusion:

c.

To determine

You will investigate the graphs of linear inequalities on a coordinate plane.

Graphical : Plot each point from the table that made $f(x)\ge x-1,$ a true statement on the graph in red .Plot each point that made $f(x)\le x-1,$ a true statement in blue.

Answer to Problem 44SR

  

Explanation of Solution

Given: Plot each point from the table that made $f(x)\ge x-1,$ a true statement on the graph in red .Plot each point that made $f(x)\le x-1,$ a true statement in blue.

  

Calculation:

Conclusion:

d.

To determine

Logical : Make a conjecture about what the graphs of $f(x)\ge x-1,$ and $f(x)\le x-1,$ look like. Complete the table with other points to verify your conjecture.

Answer to Problem 44SR

The graph of $f(x)\ge x-1,$ is the graph of $f(x)=x-1,$ and then shaded above the line. The graph of $f(x)\le x-1,$ is the graph of $f(x)=x-1,$ and then shaded below the line .

Explanation of Solution

Given: Make a conjecture about what the graphs of $f(x)\ge x-1,$ and $f(x)\le x-1,$ look like. Complete the table with other points to verify your conjecture.

Calculation:

The graph of $f(x)\ge x-1,$ is the graph of $f(x)=x-1,$ and then shaded above the line. The graph of $f(x)\le x-1,$ is the graph of $f(x)=x-1,$ and then shaded below the line .Complete the table with other to verify that this is true:

Point	$f(x)\ge x-1.$	True/false	$f(x)\le x-1.$	True/false
(5,0)	$0\ge 5-1$	false	$0\le 5-1$	true
(5,2)	$2\ge 5-1$	false	$2\le 5-1$	true
(0.1)	$1\ge -0-1$	true	$1\le 0-1$	false
(-2,-1)	$-1\ge -2-1$	true	$-1\le -2-1$	false
(1,-2)	$-2\ge 1-1$	false	$-2\le 1-1$	true

e.

To determine

Logical : Use what you discovered to describe the graph of a linear inequality.

Answer to Problem 44SR

If a linear inequality is of the form $f(x)\ge mx+b,$ then it will be the graph of $f(x)=mx+b,$ then shaded above the line . If it is in the form $f(x)\le mx+b,$ then it will be the graph of $f(x)=mx+b,$ then shaded below the line.

Explanation of Solution

Given: : Use what you discovered to describe the graph of a linear inequality.

Calculation:

If a linear inequality is of the form $f(x)\ge mx+b,$ then it will be the graph of $f(x)=mx+b,$ then shaded above the line . If it is in the form $f(x)\le mx+b,$ then it will be the graph of $f(x)=mx+b,$ then shaded below the line.