Open Up Resources Logo

Lesson 5 The Tortoise and the Hare Solidify Understanding

Ready

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.

1.

2.

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

3.

A continuous graph that ascends from (-3.2, 0.4) to (-0.4, 2), then descends from (-0.4, 2) to (1.6, -3.2)x–2–2–2222y222000

4.

5.

A continuous graph that begins at (-0.8, -0.6) curving down to (1, -0.8) where it curves up to (2.8, 3.2). A second graph in the same coordinate plane beginning at (0.8, -3.2) curving up to (1.7, -1.8) where it turns and curves down to (5.2, -2.8).x222444y–2–2–2222000

6.

A continuous graph that begins at (-2.5, -5), curves up to (-1.25, 3.2), changes direction curving down to (1.2, -3), changes direction curving up to (2.5, 5)xy

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.

a curved line B and a straight line A are graphed on a coordinate plane. the x axis is time in minutes and the y axis is distance in miles. Time (minutes)555101010Distance (miles)555101010151515000Figure 1

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 curved line B, another curved line C, and a straight line A are graphed on a coordinate plane. the x axis is time in minutes and the y axis is distance in miles. Time (minutes)555101010151515202020Distance (miles)555101010151515000Figure 2

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.

13.

Domain:

Range:

A line segment with closed endpoints at (-1, -1) and (1, 3)x–2–2–2–1–1–1111y–1–1–1111222333000AAABBB

14.

Domain:

Range:

A line that enters the given coordinate plane from (-2, 3) descends to (3, -1) where it turns sharply and extends through (4, 2) and off the grid.x–1–1–1111222333444y–1–1–1111222000AAA

15.

Domain:

Range:

A curve that enters the given coordinate pane from (-4, 5.25) curving down to (2, 2) then turning sharply, changing directions, until it leaves the given plane at (-4, -2)x–2–2–2222y–2–2–2222444000

16.

Domain:

Range:

An ellipse that extends from (-4, 0) to (2, 0) at its longest diameter and from (-1, 2) to (-1, -2) at its shorted diameter.x–4–4–4–2–2–2222y–2–2–2222000

17.

Domain:

Range:

A line segment with closed endpoints at (-6, -2) and (2, -2)x–6–6–6–4–4–4–2–2–2222y–2–2–2222000

18.

Domain:

Range:

A line segment with a closed endpoint at (2, 2) and an open endpoint at (2, 6)x–1–1–1111222333y111222333444555666000

19.

Domain:

Range:

A continuous line without endpoints that passes through (-1, 5), (0, -2), (1, 1), (2, 4), and 3, 7)x–5–5–5555y–5–5–5555000

20.

Domain:

Range:

Five plotted points (-1, 5), (0, -2), (1, 1), (2, 4), and 3, 7)x–5–5–5555y–5–5–5555000

21.

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