Math Problem Statement

If 

y = f(x)

 in the figure, find the following.

The x y-coordinate plane is given. The curve enters the window at the point (−6, −6), goes down and right, changes direction at the approximate point (−5.4, −6.2), goes up and right, changes direction at the approximate point (−2.6, −1.8), goes down and right, changes direction at the approximate point (−1.4, −2.2), goes up and right, crosses the y-axis at the origin, changes direction at the approximate point (1.4, 2.2), goes down and right, passes through the point (2, 2), changes direction at the approximate point (2.6, 1.8), goes up and right, passes through the point (5, 6), changes direction at the approximate point (5.4, 6.2), goes down and right, changes direction at the approximate point (6.6, 5.8), goes up and right, passes through the point (9, 10), changes direction at the approximate point (9.4, 10.2), goes down and right, changes direction at the approximate point (10.6, 9.8), goes up and right, and exits the window at the point (12, 12).

(a)    

f(9) = 

(b)    

f(5) = 

Solution

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Function Analysis
Curve Sketching

Formulas

f(x) = y

Theorems

Intermediate Value Theorem
First Derivative Test

Suitable Grade Level

Grades 10-12