A pumpkin pie recipe says to bake the pie at \(425^\circ \text{F}\) for 15 minutes, and then to adjust the temperature down to \(350^\circ \text{F}\) for 45 additional minutes. The function \(P\) gives the oven temperature setting \(P(t)\), in degrees Fahrenheit, \(t\) minutes after the pie is placed in the oven.

1. Explain what \(P(30)=350\) means in this context.
2. Diego discovers that the temperature inside the oven is always 25 degrees warmer than the oven’s temperature setting. The function \(B\) gives the actual temperature of Diego’s oven. If \(P(30)=350\), then what is the corresponding point on the function \(B\)?
3. Write an expression for \(B\) in terms of \(P\).

The graph shows the height of a tennis ball \(t\) seconds after it has been hit.

Graph of a function, no grid, origin O.  Horizontal axis 0 to 3, by 1’s, labeled time, seconds. Vertical from 0 to 20, by 5’s, labeled height, feet. Function starts at 0 comma 5, curves upwards and to the right until 0 point 5 comma 12, then curves downwards until hitting the horizontal axis just after 1.  

The function \(f\) given by \(f(t) = 5 +30t - 32t^2\) models the height of the ball in feet.

1. How high was the ball when it was hit? Where do you see this in the equation?
2. Suppose a second ball follows the same trajectory but is hit from 7 feet off the ground. Sketch the graph of the height of the second ball on the same axes.
3. Write an equation for a function \(g\) that defines the height \(g(t)\), in feet, of the second ball hit from 7 feet off the ground in terms of \(f(t)\).

Does the function \(f\) or the function \(g\) fit the data better? Explain your reasoning.

Functions f and g and set of data on x y coordinate, no grid, origin o. 6 tick marks on horizontal axis, 4 tick marks on vertical axis. Function f, linear moving upwards and to the right, passing through 1 point. 12 points below, 2 points above line. Function g moving upwards and to the right, 11 points just below line, passes through 2 points, 2 points just above line.