Review question

# Which of these graphs shows the area $A(c)$ as $c$ varies? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9617

## Suggestion

Shown below is a diagram of the square with vertices $(0, 0), (0, 1), (1, 1), (1, 0)$ and the line $y = x+c$. The shaded region is the region of the square which lies below the line; this shaded region has area $A(c)$.

What values of $c$ give a positive area?

When will the area be growing quickly and when slowly?

Which of the graphs given are in line with this?

Alternatively; can we come up with an explicit formula for $A(c)$, one that tells us what $A(c)$ is terms of $c$?

Could we consider the two cases $-1 \leq c \leq 0$ and $0 \leq c \leq 1$ separately?

What shape would the graph of such a formula be?