b Where does the graph intercept the x- and y-axes?
A
aDomain: 0≤ t ≤ 20
Range: - 10 000 ≤ h ≤ 0 Graph:
B
b See solution.
Practice makes perfect
a We will begin by recalling that all linear equations can be written in slope-intercept form.
y=mx+b
In this form m is the slope and b is the y-intercept. Let's look at the given equation.
h(t) = 500t - 10 000
We can see that the slope is 500 and that - 10 000 is the y-intercept. Let's graph the function using this information. First, we have to plot the y-intercept and then use the slope to find a second point. Finally we will draw a line that passes through those points.
Notice that the time must be greater than or equal to 0. The elevation h is below sea level, so it must be less than or equal to 0. Using this information we can get the graph of the function.
The domain is the set of all possible values for the independent variable. In our case, t can have any value from 0 to 20, so we can write the domain of h as an interval.
0 ≤ t ≤ 20
Similarly, the range is the set of all possible h-values. Let's write the range as an interval.
- 10 000≤ h≤ 0
b Let's recall the information we determined from Part A.
&Slope:500
&x-intercept:-10 000
&y-intercept:20
The slope of the function is 500. This tells us the ascending speed of the submersible. The y-intercept is -10 000 and tells us that the submersible starts ascending at a height of -10 000 feet. The x-intercept is 20, which means that the submersible reaches sea level in 20 minutes.
