Question

Height of Grass A home owner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period beginning on a Sunday.

Short answer

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

Step-by-step solution

Step 1. Use the definition of functions.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

Step 2. Analyze the information given.

We are given that A home owner mows the lawn every Wednesday afternoon.

Step 3. Evaluate the function.

Since this is hypothetical situation we will come up with height of grass four weeks. Let the heights at the first week be 80cm and then in the next week it is 70 cm and then 60 and 50 cm’s respectively.

Thus if we assume$t$ to be the number of week we can construct a function table as shown:

Time $t$in weeks	Height$h\left(t\right)$ in centimeters
1	80
2	70
3	60
4	50

Step 4. Graph the function.

Using the table values above, we can construct a graph as shown: