The height in feet of a soccer ball that is kicked can be modeled by the function
f(t) = 8t² + 24t, where t is the time in seconds after it is kicked. What is the domain of this function?
The domain is normally the set of xvalues, but in this case it is the set of tvalues. That is the time that the ball is in the air.
Set f(t) equal to zero, and solve for t. f(t) = 0 represents the ball being in contact with the ground. When the height of the ball is zero. 8t² + 24t = 0 {set f(t) equal to zero} 8t(t  3) = 0 {factored 8t out} 8t = 0 or t  3 = 0 {set each factor equal to zero} t = 0 or t = 3 {solved each equation for t} The domain would be the set of values from 0 to 3. That is the time the ball is in the air after being kicked. Ask the House
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