Jessica graphs the functions [math]f(x)=3|x-4|[/math] and [math]g(x)=3log_{10}(5x)[/math] to find the points of intersection. She sees that one point of intersection occurs between [math]x=2.5[/math] and [math]x=3[/math]. She also notices that, in this interval, [math]f(x)[/math] is decreasing and [math]g(x)[/math] is increasing. Next, she creates the following table of values.
| [math] \ \ \ \ \ \ \ \ \mathbf{x} \ \ \ \ \ \ \ \ [/math] | [math] \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ [/math] | [math] \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ [/math] |
|---|
| [math]2.6[/math] | [math]4.200[/math] | [math]3.342[/math] |
| [math]2.7[/math] | [math]3.900[/math] | [math]3.391[/math] |
| [math]2.8[/math] | [math]3.600[/math] | [math]3.438[/math] |
| [math]2.9[/math] | [math]3.300[/math] | [math]3.484[/math] |
What can she determine from this table of values?
-
More information is needed to make any conclusion.
-
The intersection point lies on [math]2.6 < x < 2.7[/math].
-
The intersection point lies on [math]2.7 < x < 2.8[/math].
-
The intersection point lies on [math]2.8 < x < 2.9[/math].
