Question

The function d(s) = –5s – 15 models the depth, in feet, of a rock that Dante dropped into a lake s seconds after he lost sight of the rock. What is the meaning of the x-intercept?

Answer 1

The x-intercept will tell you how many seconds have passed before Dante lost sight of the rock.

Explanation:

The problem specifies that the function d(s) will model the depth in feet of a rock that Dante dropped into a lake s seconds after he lost sight of the rock.

In this case we are using an s instead of the x, so the x-intercept will represent a given time. We can find the x-intercept by setting the function equal to zero, like this:

-5s-15=0

when solving for s we get:

`-5s=15`

`s=-(15)/(5)`

s=-3

This means that Dante dropped the ball into a lake 3 seconds before he lost sight of the rock. This is what the negative stands for, some time in the past.

So the x-intercept tells us the time it took for Dante to lost sight of the rock.