For the following functions, determine domain and range. Round to two decimals where necessary.
On the right you see the graphs of two functions and with and , using the standard window settings.
Algebraically determine the zeros of .
The standard window settings are not that useful if you want to see the `x` -intersects and vertices of both functions. Choose better window settings to determine the vertices of .
Determine the range of both functions.
Determine the intersection points of the two graphs of and algebraically .
A firework is launched from ground level. Its height above ground level is subsequently dependent on time, until it explodes. The following function describes the trajectory: . In this formula is the height above ground level in meters, and is the time in seconds.
The firework explodes after seconds. What is the maximum height it can reach?
Write down the domain and range of this function, taking the context into account.
At what height did the firework explode?
How long (in seconds) would the firework be visible above a row of trees with a height of m?
Why does the graph above not show the trajectory of the firework?
Every week, a trader can sell up to pieces of a certain product. He has no competition, and therefore the number of items he sells is only dependent on the price he chooses. He finds the following relationship: .
Write down a formula of the revenue as a function of price .
What values are possible for ?
What values are possible for ?
Given the function with and domain .
Determine the range of .