Section 1.1 Functions

Objective By following instructions students will be able to: Decide whether relations between two variables are functions. Use function notation and evaluate functions. Find the domain of functions. Use functions to model and solve real-life problems.

Example 1: Decide whether the description represents y as a function of x. The input value x is the number of representatives from a state and the output value y is the number of sentators. Table c) Input x 2 3 4 5 Output y 11 10 8 1

Example 2: Which of the equations represents y as a function of x? a) b)

Example 3: Let and find g(2) b) g(t) c) g(x+2)

Example 4: Evaluate the function when x=-1, 0, and 1.

Example 5: Find the domain of each function. a) b) c) d) Volume of a sphere: e)

Example 7: A baseball is hit at a point of 3 feet above ground at a velocity of 100 feet per second and an angle of 45 degrees. The path of the baseball is given by the function Where y and x are measured in feet. Will the baseball clear a 10- foot fence located 300 feet from home plate?

Example 8: The money C (in billions of dollars) spent for direct mail advertising in the United States increased in a linear pattern from 1990 to 1992. Then in 1993, the money spent took a jump and, until 1996, increased in a different linear pattern. These two patterns can be approximated by the function Where t=0 represents 1990. Use this function to approximate the total amount spent for direct mail advertising between 1990 and 1996.

Revisit Objective Did we… Decide whether relations between two variables are functions? Use function notation and evaluate functions? Find the domain of functions? Use functions to model and solve real-life problems?

Homework HW: I: pg 67 #s 7ab, 19 (domain/range?) II:pg 82 #s 1-7, 10-20 Even, 25, 29, 33, 35, 37, 38, 43-55 ODD III: pg 87 #s 103-107