A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below) represents this situation where x is time and y is the distance off of the ground.

e. What would the new function be? What kind of transformation is this?
f. Would you still use the same domain and range? Why or why not?

Answer:

a) The domain of the function is    . , , b)The range of the function is . , , c) The ball is 73 meters off of the ground at x = 3 seconds.Step-by-step explanation:The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function represents this situation where x is time and y is the distance off of the ground. a) What domain does the function make sense? b) What range does the function make sense ? c) How far off the ground is the ball at time x = 3 seconds?a) Let  and  be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when  and . That is: Therefore, the domain of the function is    . , b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is . , c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:The ball is 73 meters off of the ground at x = 3 seconds. 

Step-by-step explanation:

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