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Type: Multiple-Choice
Category: Functions and Relations
Level: Grade 11
Standards: HSA-REI.D.11
Author: nsharp1
Created: 6 years ago

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Simone sketches the functions

$f(x) = x^3 + 4x^2 + 2x - 9$ and

$g(x) = e^(x-5) - 7.$ She sees that one of the intersection points occurs between

$x=-4$ and

$x=-2.$ She also notices that, near this intersection point, to the left of the intersection point,

$f(x)$ is below

$g(x)$ on the graph, and to the right of the intersection point

$f(x)$ is above

$g(x)$ .

Grade 11 Functions and Relations CCSS: HSA-REI.D.11

If Simone continues to choose values of

$x$ in the middle of each new interval (for example, she would choose

$x=-2.5$ if she looks in the interval

$-3 < x < -2$ ), what would be a reasonable criterion for believing that she has found an accurate point of intersection and why?

$|f(x)|$ is very small, because the $x$ value is very precise.
$|g(x)|$ is very small, since $x$ is near the middle of the interval.
$(|f(x)+g(x)|)/2$ is near zero, as you've averaged the absolute value of the functions and the functions should cancel each other out.
$|f(x)-g(x)|$ is very small, since these values should be almost equal near the point of intersection.