Answer:
1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].
2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex] of the function [tex]g(x)[/tex] shows that the line will always have the same y-coordinate.
3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function [tex]g(x)[/tex].
Step-by-step explanation:
For this exercise you need to know that the slope of any horizontal line is zero ([tex]m=0[/tex])
The slope of a line can be found with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
You can observe in the graph of the function [tex]g(x)[/tex] given in the exercise, that this is an horizontal line. Then, you can conclude that its slope is:
[tex]m=0[/tex]
The steps to find the slope of the function [tex]f(x)[/tex] shown in the table attached, are the following:
- Choose two points, from the table:
[tex](0,3)[/tex] and [tex](4,-1)[/tex]
- You can say that:
[tex]y_2=-1\\y_1=3\\\\x_2=4\\x_1=0[/tex]
- Substitute values into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]:
[tex]m=\frac{-1-3}{4-0}[/tex]
- Finally, evaluating, you get:
[tex]m=\frac{-4}{4}\\\\m=-1[/tex]
Therefore:
1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].
2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex] of the function [tex]g(x)[/tex] shows that the line will always have the same y-coordinate.
3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function [tex]g(x)[/tex].
