Given , which equation represents ?
A function is defined as , where . What is the value of ?
Consider the function . Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
What is the inverse of the function ?
What is the inverse of ?
For the function , the inverse function, , equals
If where , then the inverse of the function is
The explicit formula represents the number of seats in each row in a movie theater, where represents the row number. Rewrite this formula in recursive form.
Rewrite the formula in recursive form.
A manufacturer of sweatshirts finds that profits and costs fluctuate depending on the number of products created. Creating more products doesn't always increase profits because it requires additional costs, such as building a larger facility or hiring more workers. The manufacturer determines the profit, , in thousands of dollars, as a function of the number of sweatshirts sold, , in thousands. This function, , is given below.
Graph , over the interval , on the set of axes on the next page.
Over the given interval, state the coordinates of the maximum of and round all values to the nearest integer. Explain what this point represents in terms of the number of sweatshirts sold and profit.
Determine how many sweatshirts, to the nearest whole sweatshirt, the manufacturer would need to produce in order to first make a positive profit. Justify your answer.
The inverse of is