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**Unformatted text preview: **MAC1105 Activity 4 Name: ______________ ___ Fall, 2011 Period: (circle yours) TH 11:00 TH 12:30 TH 2:00 Show algebraic details in spaces provided, and confirm answers with the calculator. 1. The table below shows the output for functions f and g for input x-values 0, 1, 2, and 3. a) Complete the table by calculating the average rate of change over the last two-unit input interval for each function. Which is function is linear, f or g ? ______ x = 0 x = 2 x = 4 x = 6 x = 8 f(x) 2 6 10 14 18 average rate of change of f over input interval … … [0,2] 6 2 2 2 0 m- = =- … [2,4] 10 6 2 4 2 m- = =- … [4,6] 14 10 2 6 4 m- = =- … [6,8] g(x) 2 6 18 38 66 average rate of change of f over input interval … … [0,2] 6 2 2 2 0 m- = =- … [2,4] 18 6 6 4 2 m- = =- … [4,6] 38 18 10 6 4 m- = =- … [6,8] b) Fact : The average rate of change of a quadratic function increases or decreases by a constant amount over equal input intervals. Complete this sentence: g is quadratic because over two-unit input intervals the average rate of change of g _________________________ by the constant amount ____. ( increases or decreases ? ) 2. As an experiment in motion acted on only by the force due to gravity, a stone is thrown upward from a bridge and we time it as it falls to the water below. The height, h , in feet above the water t seconds from the moment it’s released is given by the quadratic function ( ) 2 16 32 48 h t t t = - + + . a) Find ( ) h and write a sentence that interprets the answer. Use appropriate units. b) Find the time it takes for the rock to reach its maximum height above the water, and find this maximum height. Record answers below using appropriate units. time to max height: t = ____________________ max height: t = ____________________ c) Find the time when the rock impacts the water. time to impact : t = ____________________ d) Sketch the function from launch to impact with the ground, labeling the vertical intercept, horizontal intercept, and the vertex with ordered pairs. e) Over what time interval is height increasing? ______________________ f) State the domain and range for this experiment. Domain: ___________________________ Range: _____________________________ MAC1105 Activity 4 Name: ______________ ___ Fall, 2011 Period: (circle yours) TH 11:00 TH 12:30 TH 2:00 Show algebraic details in spaces provided, and confirm answers with the calculator. 1. The table below shows the output for functions f and g for input x-values 0, 1, 2, and 3. a) Complete the table by calculating the average rate of change over the last two-unit input interval for each function. Which is function is linear, f or g ? ______ x = 0 x = 2 x = 4 x = 6 x = 8 f(x) 2 6 10 14 18 average rate of change of f over input interval … … [0,2] 6 2 2 2 0 m- = =- … [2,4] 10 6 2 4 2 m- = =- … [4,6] 14 10 2 6 4 m- = =- … [6,8] g(x) 2 6 18 38 66 average rate of change of f over input interval … … [0,2] 6 2 2 2 0 m- = =- … [2,4] 18 6 6 4 2 m- = =- … [4,6] 38 18...

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