Question

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Answer 1

Answer:

1) The slope of the function $g(x)$ is $0$ and the slope of the function $f(x)$ is $-1$.

2) The negative slope of the function $f(x)$ shows that it is the line is increasing and the slope $0$  of the function  $g(x)$  shows that the line will always have the same y-coordinate.

3) The slope of the function is $f(x)$ is greater than the slope of the function  $g(x)$.

Step-by-step explanation:

 For this exercise you need to know that the slope of any horizontal line is zero ($m=0$)

The slope of a line can be found with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

You can observe in the graph of the function  $g(x)$  given in the exercise, that this is an horizontal line.  Then,  you can conclude that its slope is:

$m=0$

The steps to find the slope of the function $f(x)$ shown in the table attached, are the following:

- Choose two points, from the table:

$(0,3)$ and $(4,-1)$

- You can say that:

$y_2=-1\\y_1=3\\\\x_2=4\\x_1=0$

- Substitute values into the formula $m=\frac{y_2-y_1}{x_2-x_1}$:

$m=\frac{-1-3}{4-0}$

- Finally, evaluating, you get:

$m=\frac{-4}{4}\\\\m=-1$

Therefore:

1) The slope of the function $g(x)$ is $0$ and the slope of the function $f(x)$ is $-1$.

2) The negative slope of the function $f(x)$ shows that it is the line is increasing and the slope $0$  of the function  $g(x)$  shows that the line will always have the same y-coordinate.

3) The slope of the function is $f(x)$ is greater than the slope of the function  $g(x)$.