Neatly print first and last names: Exam II. "On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.

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1 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 1 Neatly print first and last names: Lecture Time:!! 12:45 PM!!! 2:20 PM!! (Circle one.) Exam II "On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work." Signature of student My signature in this blank allows my instructor to place my exam in a stack near the front of the room where I will pick it up on the day they are returned. Signature of student 1. No calculators are allowed. 2. You are authorized to use a pencil, eraser, and your own TAMU ID; use of anything else is a violation of the Aggie Honor Code. 3. All cell phones must be turned off and placed in your backpack. 4. Write all solutions in the space provided as full credit might not be given without complete, correct accompanying work, even if the final answer is correct. 5. Intervals should be stated in interval notation. 6. Continuing to write on the exam after time is called is considered cheating. 7. You may not discuss the contents of the exam with anyone until the exam is returned in class.

2 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 2 (1 point) NEATLY PRINT FIRST AND LAST NAMES: (1 point) LECTURE TIME:! 12:45 PM!!! 2:20 PM!! (Circle one.) PAGE 2 PAGE 3 PAGE 4 PAGE 5 PAGE 6 PAGE 7 PAGE 8 PAGE 9 PAGE 10 PAGE 11 PAGE 12 TOTAL

3 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 3 1. (4 points) a) If f (x) = 7x 5 + 6, then as x, f (x) b) If f (x) = 7x 5 + 6, then as x, f (x) c) If f (x) = 7x 4 + 6, then as x, f (x) d) If f (x) = 7x 4 + 6, then as, x, f (x) x + 7, x < 2 2. (2 points) If f (x) = (x + 2) 2 + 5, -2 x 1 6, 1 < x, then a) f ( 3) = b f (π ) = 3. (3 points) Determine the equation of the line perpendicular to x + 3y 6 = 0 that passes through the origin.!!!!!!!

4 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 4 4. (6 points) This is an equation of a circle: 4x 2 + 4y 2 24x + 4y + 25 = 0. The center of the circle is. The radius of the circle is. The domain of this relation is 5. (4 points) The points A ( 1, 2) and B ( 3, -2) are the endpoints of a diameter of a circle. Write the standard form of the equation of this circle.!!!!!!!

5 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 5 6. a) (2 points) State the general form of the difference quotient. DQ(x, h) = b) (4 points) Now apply it to the function f ( x) = x 2 + 5x and fully simplify. 7. (6 points) Consider the relation (x +1) 2 + ( y 3) 2 = 10. List the coordinates of the x -intercept(s) (If there are none, write NONE.) y -intercept(s) (If there are none, write NONE.)

6 Fry Texas A&M University! Math 150 Precalculus Fall 2015! 6 8. As part of a holiday tradition physics students went to the roof of the building and fired an orange projectile straight up into the air. They were able to determine that the height in feet of the projectile could be described by the function f (t) = 16t t + 96 where t is time in seconds after the projectile was fired into the air. a) (1 point) How tall was the building? ft b) (5 points) How high did the projectile go? ft c) (4 points) How long until it smashed onto the ground? sec 9. (10 points) Let f (x) = x and g(x) = x 2 1 a) ( f! g) ( x) =! b) The domain of ( f! g) ( x) is c) f g x ( ) =! d) The domain of f g x ( ) is

7 Fry Texas A&M University! Math 150 Precalculus Fall 2015! (5 points) You are part of a wilderness relay race team. You will be placed on an island four miles from shore. Your leg of the race involves getting from the island to a cabin on the shore that is 7 miles north of the island. (See diagram.) In training it was determined that you could row at a rate of 3 miles per hour and travel along the rocky shore at a rate of 5 miles per hour. It will be important to choose a route that minimizes your time to the cabin. You start your calculations by assuming that you will aim for a spot on the shore that is x miles north of the point directly east of the island. (See diagram.) Given this plan, write a function T (x) that describes how many hours it will you to get to the cabin. 4 x 7 T (x) = 11. (5 points) The hot water pipe call fill the pool in 12 hours while the cold water pipe can fill the pool in 9 hours. When both pipes are used, how many hours does it take to fill the pool? a) b) 5 1 7! c) d) 6 e) None of these

8 Fry Texas A&M University! Math 150 Precalculus Fall 2015! a) (5 points) Let f 1 be the inverse function of f (x) = 2x + 5. f 1 (x) = When fully simplified, i) 2x ii) 1 iii) 3 5x 2x! iv) 3 5x 2xy v) None of these b) (2 points) The domain of f (x) = 3 2x + 5 is, c) (2 points) while the range of f (x) = 3 2x + 5 is.

9 Fry Texas A&M University! Math 150 Precalculus Fall 2015! Here is the graph of f (x) = x3 1 8 a) (2 points) Looking at the graph, you judge that the function is one-to-one because it passes (Circle one): i) the vertical line test ii) the horizontal line test iii) the equivalency test iv) the cubic test v) the cube root test. b) (2 points) Fill in the blanks of this definition: A function f (x) is one-to-one if implies that c) (2 points) Write a short proof showing that f (x) = x3 1 8 is indeed a one-to-one function.

10 Fry Texas A&M University! Math 150 Precalculus Fall 2015! (6 points) Fill in the blanks: a) f (x) is an even function if f ( x) = x in the domain of f (x) b) Even functions are symmetric about the c) f (x) is an odd function if f ( x) = x in the domain of f (x) d) Odd functions are symmetric about the e) To demonstrate algebraically that the graph of a relation is symmetric about the x -axis we start by substituting for into the equation that describes the relation. 15 (2 points) Demonstrate algebraically if the graph of ( x 1) 2 + y 2 = 9 is symmetric about the x -axis 16. (4 points) Determine algebraically if the function f (x) = x4 1 x 3 is even, odd, or neither.!! Circle one: f (x) is!! even!!! odd!!! neither

11 Fry Texas A&M University! Math 150 Precalculus Fall 2015! (10 points) f (x) = x has been transformed to yield g(x) = 4 9 x! a) domain of g(x)! b) range of g(x) c) anchor point of g(x) d) y -intercept for g(x) e) x -intercept(s) for g(x) e) Include the points you found above in the sketch of the graph of g(x) = 4 9 x f) list the transformation(s) performed on f (x) to yield g(x) (order matters)

12 Fry Texas A&M University! Math 150 Precalculus Fall 2015! (6 points) Given the graph of the function below, determine the following (If there are none, write NONE.) a) domain b) range c) interval(s) on which the function is decreasing d) minimum value of the function e) maximum value of the function