# Lesson 5The Tortoise and the HareSolidify Understanding

Identify which of the following representations are functions. If the representation is NOT a function, state how you would fix it to make it a function.

### 2.

The number of calories you have burned since midnight at any time during the day.

### 4.

 $x$ $f\left(x\right)$ $-12$ $-8$ $-6$ $-4$ $25$ $25$ $25$ $25$

## Set

The graph in Figure 1 shows time (minutes) on the -axis and distance (miles) on the -axis for cars traveling in the same direction along the freeway. The graph for Car A is a straight line. The graph for Car B is a parabola because it is a quadratic function.

### 7.

Which car has the cruise control on (is maintaining at the same speed)? How do you know?

### 8.

Which car is accelerating? How do you know?

### 9.

Identify the interval in Figure 1 where car A has gone farther than car B.

### 10.

The graph of the speed of a third car, Car C, which has an exponential relationship is now shown in the graph (see Figure 2). All 3 cars have the same destination.

#### a.

If the destination corresponds with a distance of miles from the origin, which car do you predict will arrive first? Justify your answer.

#### b.

If the three cars passed the starting point at the same time, and were racing, would there ever be another time that they would be tied? Explain.

#### c.

Describe the race for these three cars.

### 11.

If the cars are able to proceed beyond a time of minutes, according to the type of function they are being described by, will the lead ever change again? Explain.

### 12.

On a graph that shows distance versus time, what do you look at in order to find speed?

## Go

State the domain and range of each graph. Use interval notation where appropriate.

Domain:

Range:

Domain:

Range:

Domain:

Range:

Domain:

Range:

Domain:

Range:

Domain:

Range:

Domain:

Range:

Domain:

Range:

### 21.

Are the domains of #19 and #20 the same? Explain.