Question

In two or more complete sentences, compare the slopes of the two functions. In your comparison, include which function has the greatest slope. The functions fx and gx are shown below. Table of : x f(x) -4 7 -2 5 0 3 2 1 4 -1 Graph of :g(x)

Answer 1

I guess we have the table:

x f(x)

-4 7

-2 5

0 3

2 1

4 - 1

To find the slope of this, we need to select two different points (x1, y1) and (x2, y2) and use the relation:

slope = (y2 - y1)/(x2 - x1)

let´s use the first two:

(-4,7) and (-2, 5)

Slope = (5 - 7)/(-2 - (-4)) = -2/2 = -1

Now, if we want to be sure that this is a linear equation, we should do the same for other two pairs of points, now use the first and the third:

(-4, 7) and (0,3)

S = (3 - 7)/(0 -(-4)) = -4/4 = -1

Now, for the function g(x) we can see a constant line, that is parallel to the x-axis.

This means that the slope of this function is equal to zero.

This means that the slope of g(x) is bigger than the slope of f(x), because 0 > 1