interpreting key features

Question

Example 1: Joe is painting and selling artwork to raise money for a road trip. He has $75 to spend on enough art supplies to last him through 12 paintings and plans to sell each painting for $25.

What is the domain of the function?

What does it represent in the context of the problem?

What is the rate of change?

What does it represent in the context of the problem?

What is the x-intercept?

What does it represent in the context of the problem?

What is the y-intercept?

What does it represent in the context of the problem?

Over which interval, if any, is the function positive?

What does it represent in the context of the problem?

Over which interval, if any, is the function negative?

What does it represent in the context of the problem?

Answer 1

The domain of the function is the number of paintings he possibly sells. That is the integers 0 - 12.

Incidentally, the range of the function can be thought of as his cash in hand.

The rate of change is how much income he gets per painting sold ($25)

x - intercept would be 3 (the number of paintings needed to break even)

y intercept is -$75 (the cost of his materials)

When x> 3, f(x) is positive. f(x) represents his profit

When x<3, f(x) is negative. f(x) represents his loss