Essential Calculus
2nd Edition
ISBN: 9781285209067
Author: Stewart
Publisher: Cengage
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The circumference, C, of a circle increases as the radius, r, of the circle increases over time. What function composition represents the circumference, C, of a circle as a function of the radius, r, at time t? Recall that the circumference of a circle with radius r is C=2πrC=2πr.
What equation represents the transformed function g (x) that is formed by shifting the graphed of  f(x) = |x| right 2 units and up 5 units.

10 Find the composition of the function.
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- The height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?arrow_forwardWhen examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?arrow_forwardThe initialsize of a culture of bacteria is 1000. After 1 hour the bacteria count is 8000. (a) Find a function n(t)=n0en that models the population after s hours. (b)Find the population after 1.5 hours. (c)After how many how will the number of bacteria reach 15,000? (d)Sketch the graph of the population function.arrow_forward
- When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?arrow_forwardUse your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.arrow_forward44. The behaviour of tides in a fishing community can be modelled using the function below, where h represents the height of the tide, in metres, at t hours after noon. What is the height of the tide at 5 p.m.?arrow_forward
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