Please open your laptops, log in to the MyMathLab course web site, and open Quiz 3.6A.

1. You will have access to the online calculator on your laptop during this quiz. No other calculator may be used. Please open your laptops, log in to the MyMathLab course web site, and open Quiz 3.6A. • IMPORTANT NOTE: If you have time left after you finish the problems on this quiz, use it to check your answers before you submit the quiz! • Remember to turn in your answer sheetto the TA when the quiz time is up.

2. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

3. Section 3.6BMore About Functions:Functions that are non-linear, i.e. that can’t be represented in the form Ax + By = C

4. Example y f(x) x f(0) = f(4) = f(-5) = f(-6) = Given the graph of the following function, find each function value by inspecting the graph. 2 3 -1 -7

5. The open circles indicate points that are not included in the relation. • The filled circles indicate points that areincluded in the relation. • Reading the graph: • A package that weighs more than 4 ounces but no more than 5 ounces costs $1.50 to mail • We can also interpret this graph using an inequality or interval notation to express parts of the domain: • A package whose weight falls within the interval (4,5] costs $1.50 to mail. • Or, package whose weight x is in the interval 4 < x ≤ 5 will cost $1.50 to mail. This graph represents the cost of mailing a large envelope through the postal service by weight.

6. To answer this question, use the vertical line test. • There is no vertical line that will intersect more than one point of the graph at a time, so this relation IS a function. • Practically speaking, this means that there can’t be more than one price assigned to any one weight: A 4-ounce package costs about $1.35 to mail; a 4.2 ounce package costs $1.50 to mail. • This kind of function is called a piecewise-defined function. Does the relation depicted by this graph satisfy the definition of “function”?

7. y xy x (0, 0) (-2, 2) (2, 2) (1, 1) (-1, 1) Example: Is this a function? Example: Is this a function? Graph y = | x |. 2 2 1 1 0 0 – 1 1 ANSWER: Yes, so we can write it as f(x) = | x|, which is the absolute value function. 2 – 2

8. y xy (2, 8) (-2, 8) x (-1, 2) (1, 2) (0, 0) Example: Is this a function? Graph y = 2x2. 2 8 2 1 0 0 – 1 2 – 2 8 ANSWER: Yes, so we can write it as f(x)=2x2, which is a quadratic function.

9. Evaluating a function for a variableinstead of a number: Example: Evaluate f(x) = 2x + 5 for: x = 6: f(6) = 2*6 + 5 = 12+ 5 = 17. x = t: f(t) = 2*t+ 5 = 2t + 5 x = p: f(p) = 2*p + 5 = 2p + 5 x = h + 3: f(h +3) = 2*(h + 3) + 5 = 2*h + 2*3 + 5 = 2h + 6 + 5 = 2h + 11

10. Evaluating a function for a variableinstead of a number: Example 2: Evaluate f(x) = x2 + 1 for: x = 6: f(6) = 62 + 1= 36 + 1 = 37 . x = t: f(t) = t2 + 1 x = p: f(p) = p2 + 1 x = h + 3: f(h +3) = (h + 3) 2+ 1 = (h+3)(h+3) + 1 = h2 +3h +3h +3*3 + 1 = h2 + 6h + 10

11. The assignment on this material (HW 3.6B) is due at the start of the next class session, and there will be a short quiz on it as usual, either at the start or end of the class session. Lab hours: Mondays through Thursdays 8:00 a.m. to 6:30 p.m.

12. You may now OPEN your LAPTOPS and begin working on the homework assignment. We expect all students to stay in the classroom to work on your homework till the end of the 55-minute class period. If you have already finished the homework assignment for today’s section, you should work ahead on the next one or work on the next practice quiz/test.