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**Additional info for Master the AP Calculus AB & BC (Peterson's Ap Calculus Ab & Bc)**

**Example text**

Are you telling me I can’t use it on the AP test? Sorry, but you can’t. By the way, I shudder to think about how the toenail clippings were put to use. com detailed explanation. 8 PART I: AP Calculus AB & BC Basics ................................................................. Only in the four listed circumstances can you use the calculator to reach an answer. For instance, most calculators can find the maximum or minimum value of a function based on the graph, but you cannot use a calculator as your justification on a problem such as this.

The graph of h(x) 5 2x2 2 3, with no restriction, has two roots. reverse ordered pairs, h21 SÎ D S Î D S ÎD S ÎD 3 ,0 . Because inverse functions 2 3 3 must include the points 0, and 0,2 . If this 2 2 Easily found, the two roots are 3 ,0 2 and 2 were allowed, h21 would have two outputs for the domain element 0 and, therefore, could not be a function. The visual test used to ensure that a function has an inverse is called the horizontal line test, and it works much like the vertical line test. If any horizontal line drawn through a function graph intersects the graph at more than one place, the function cannot have an inverse.

Solution: The graph begins as the parabola x2, but once x 5 21, the new rule takes over, and the graph becomes the horizontal line y 5 2. This line stops, in turn, at x 5 2. The function is undefined between x 5 2 and x 5 3, but for all x . 3, the line 2x 2 4 gives the correct outputs. Note: If you didn’t recognize that y 5 x2 is a parabola, that’s OK (for now). Later in the chapter, we discuss how to recognize these graphs. h(22) 5 (22)2 5 4, since 22 falls within the definition of the first of the three rules.