We included **H****MH Into Math Grade 8 Answer Key**** PDF** **Module 6 Lesson 6 Describe and Sketch Nonlinear Functions **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 6 Lesson 6 Answer Key Describe and Sketch Nonlinear Functions

I Can convert between a verbal description of a function and its graph, and between a graph and a

verbal description of a function.

**Step It Out**

1. Emanuel walks the North Trail at his local park. The graph shows his distance from the fountain at the

center of the park as he walks along the trail. Use the graph to answer the questions.

A. Each section of the graph is (linear / nonlinear).

B. The slope for the first part of his walk is (positive / negative) which means his distance from the

fountain is (increasing / decreasing) at a constant rate.

C. The slope for the second part of his walk is ____. What does that mean about his distance from the

fountain?

_________________________

D. The slope for the third part of his walk is (positive / negative), which means his distance from the fountain is (increasing / decreasing) at a constant rate.

E. Emanuel returns to the park the next day and walks the South Trail.

The South Trail graph is (linear / nonlinear).

F. Early on, does his distance from the fountain decrease at a constant rate? _____

Near the end, does his distance from the fountain increase at a constant rate? ____

How do you know? ______

Answer:

A. The linear function is a function that makes a straight line when we graph.

The nonlinear function is any function but it is not a straight line.

The graph has three sections and each section is linear.

B. The slope for the first part of his walk is negative which means his distance from the

the fountain is decreasing at a constant rate.

C. The slope for the second part of his walk is 0 then it is horizontal to the x-axis. And it is the center of the distance to the North trial.

D. The slope for the third part of his walk is positive which means his distance from the fountain is increasing at a constant rate.

E. The linear graph is a graph that makes a straight line when we graph.

A nonlinear graph is any graph but it is not a straight line.

The south Trail graph is nonlinear.

F. The distance from the fountain is not decreased at a constant rate.

The distance from the fountain is not increased at a constant rate. Because the graph is not linear.

**Turn and Talk** Describe potential scenarios for each path in relation to the fountain location.

2. When a state fair opened, the number of people attending the fair gradually increased at a constant rate in the morning. Then the number of people remained constant through the afternoon. In the evening, the attendance gradually decreased at a constant rate until near the end of the night, when the number of people decreased swiftly at a constant rate as they all left.

A. Where should the graph of the situation begin and why?

It starts at ____ because there were ____ people there until the fair opened.

B. Describe what happens to the graph as the number of people gradually increased at a constant rate in the morning. Will the slope of this part of the graph be positive or negative? Will it be steep or gradual?

It will be (positive / negative) and (steep / gradual).

C. Describe what the graph looks like as the number of people remained constant through the afternoon.

This part of the graph will be ______

D. Describe what happens to the graph as the number of people gradually

decreased at a constant rate. Will the slope of this part of the graph be

positive or negative? Will it be steep or gradual?

It will be (positive / negative) and (steep / gradual).

E. Describe what happens to the graph near the end of the night, when the number of people decreased swiftly as they all left. Will the slope of this part of the graph be positive or negative? Will it be steep or

gradual?

It will be (positive / negative) and (steep / gradual).

F. Use what you described to sketch the situation.

G. Suppose the number of people attending the fair continued to gradually increase at the same constant rate throughout the afternoon instead of remaining constant. Sketch a graph that represents this situation.

Answer:

A. It starts at increasing with constant because there was the number of people there until the fair opened.

B. The graph will be positive and steep.

C. The number of people remained constant through the afternoon.

This part of the graph is constant.

D. The slope of the graph is negative and gradual.

E. The slope of the negative then the number of people decreased swiftly as they all left and it is gradual.

F.

The graph is linear.

It is increased with constant and stay constant and decreased with constant.

3. Kevin says that this graph describes an airplane that takes off, climbs to cruising altitude, stays at the cruising altitude for the flight, and then descends for landing. Kate says that the graph better describes a model rocket that launches, rises to a maximum altitude, and then falls faster and faster until it reaches the ground.

A. Is the graph linear, nonlinear, or a combination?

_________________________

B. Is the graph increasing at a constant rate? Is the graph decreasing at a constant rate?

_______________________

C. Is there a portion of the graph where the altitude is constant?

_______________________

D. Whose description does the graph better represent, Kevin’s or Kate’s? Why?

_______________________

**Turn and Talk** Describe and sketch a graph to represent the airplane flight that Kevin suggested.

**Check Understanding**

Question 1.

Describe the temperature changes shown in the graph.

_______________

Answer:

The given graph is linear.

A linear graph is a graph that makes a straight line when we graph.

A nonlinear graph is any graph but it is not a straight line.

In the given graph There are three sections The first section is increased at a constant rate; the second section is stay constant and the third section is decreased at a constant rate.

Question 2.

Selena hikes a trail. Her elevation decreases at a constant rate until she reaches a stream. Her elevation stays the same walking by the stream until she climbs a hill at a constant rate to reach the campground. Sketch a graph to represent the situation.

Answer:

The graph is linear.

The graph has three sections the first section is decreased at a constant rate the second section has stayed constant and the third section is increased at a constant rate.

On Your Own

Question 3.

The graph represents the speed of a swimmer during a race. Describe the swimmer’s speed during the course of the race.

Answer:

Given that the graph is linear.

The speed of the swimmer during the race is firstly increased with constant rate and then stay constant and decreased slightly with constant rate.

Question 4.

The value of a stock increases gradually at a constant rate at the beginning of the day. The value quickly decreases at a constant rate to below the original value during the middle of the day. It then stays the same for the rest of the day.

A. **Model with Mathematics** Sketch a graph that represents the situation.

Answer:

The graph is linear

A linear graph is a graph that makes a straight line when we graph.

A nonlinear graph is any graph but it is not a straight line.

The graph is increased at a constant rate and decreased with a constant rate.

B. **Reason** How would the graph change if the stock gradually decreased during the middle of the day?

Answer:

Gradually means the slightly

The graph is increased at the constant rate and decreased with the slightly constant.

Question 5.

Sketch a graph that shows a value that starts increasing rapidly, then continues increasing but more gradually, then increases rapidly again.

Answer:

The graph is linear

A linear graph is a graph that makes a straight line when we graph.

A nonlinear graph is any graph but it is not a straight line.

Here the graph is increased rapidly.

**For Problems 6-9, write a situation that the graph could represent.**

Question 6.

Answer:

Given that the graph is linear

A linear graph is a graph that makes a straight line when we graph.

A nonlinear graph is any graph but it is not a straight line.

The graph has three sections the first section stays constant the second section is increased by a constant rate the third section is stay constant.

Question 7.

Answer:

Given that the graph is nonlinear.

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The graph is a curve line. The curve is constantly changing.

Question 8.

Answer:

Given that the graph is linear.

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The graph has four sections the first section is constant the second section is decreased with the constant rate the third section is staying constant and the fourth section is increased with a constant.

Question 9.

Answer:

The given graph is nonlinear.

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The graph is in the form of a curve. The directions of the curve are constantly changing.

Question 10.

Manny completes a video game level. The elevation of his video game character is constant and then increases rapidly at a constant rate to a new constant elevation. The elevation then decreases rapidly at a constant rate to a new constant elevation to complete the level. Sketch a graph that represents the situation.

Answer:

The graph is linear.

The graph has five sections it is first constant and increased with constant and stay constant and decreased with constant and at last stay constant.

**The graph represents the height of a ball over time as the ball rolls across a ledge, then falls off. Use the graph to answer Problems 11—14.**

Question 11.

Starting at what time and ending at what time, when is the graph linear?

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The given graph is starting at 0 sec and ending at 8 sec. the starting time is linear.

Question 12.

Starting at what time and ending at what time, when is the graph nonlinear?

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The given graph is starting at 0 sec and ending at 8 sec. the ending time is nonlinear.

Question 13.

What does the linear part of the graph describe?

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The linear part of the graph describes the triangle.

Question 14.

**STEM** What does the nonlinear part of the graph describe? Why is it nonlinear?

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The nonlinear part of the triangle describes the blue color bolls. It is nonlinear because the way of the balls is nonlinear.

**Use the graph to answer Problems 15—16.**

Question 15.

**Social Studies** What happens to the fish population in the spring? Use either the term linear or nonlinear in your response.

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The fish population in the spring is nonlinear.

Question 16.

A fishing competition is held on the lake once a year.

A. Which part of the graph shows the result of the competition? In what season is the competition held?

Answer:

The combination of a linear and nonlinear graph is the competition.

The competition is held in the springtime.

B. Describe what happens to the fish population after the competition. Use either the term linear or nonlinear in your response.

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

After the competition, the fish population is nonlinear because it is not a straight line.

**Lesson 6.6 More Practice/Homework**

Question 1.

**Open Ended** Write a situation that this graph could represent.

Answer: The situation represents the graph is graph is decreasing rapidly, then continues decreasing but more steeply, then decreases rapidly again.

Question 2.

Darnell participates in an obstacle course. He climbs a ladder, runs across a bridge, and then climbs down another ladder. Sketch a graph that represents his position above the ground as he completes the obstacle course.

Answer:

The graph is linear.

In the graph, there are three sections in the first section he climbs a ladder. In the second section, he crosses the bridge and in the third section, he climbs down another ladder.

So, first increased with a constant rate and stay constant, and then decreased at a constant rate.

Question 3.

**Reason** The two graphs show the speeds of bicycles as they are coming to a stop. Describe how each of the bicycles comes to a stop.

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

The bicycle A graph is linear.

Bicycle A is stopped with the speed decreasingly at a constant rate.

The bicycle B is nonlinear.

The bicycle B is stopped with constant but the constant is always changes.

**For Problems 4—5, sketch a graph that represents the given situation.**

Question 4.

The number of points Sally earns in a video game increases at a constant rate, then stays constant, and then increases at a constant rate.

Answer:

The graph is linear.

The graph has three sections the first section is increased at a constant rate second section is stay constant and the third section increases at a constant rate.

Question 5.

Rebecca drove at a constant speed on a street. She slowed at a constant rate to turn onto the highway and then accelerated at a constant rate to drive at the speed limit.

Answer:

The graph is linear.

The graph has three sections the first section is constant speed on a street and the second section is slowed at a constant rate to turn onto the highway and the third section is constant rate to drive at the speed limit.

**Test Prep**

Question 6.

Which graph is a linear function decreasing at a constant rate?

Answer:

A linear graph is a graph that makes a straight line when we graph.

The nonlinear graph is any graph but it is not a straight line.

Option B is a linear function decreasing at a constant rate from the given four graphs.

Question 7.

Select all statements that are true of the graph shown.

A. The rate of the increase is greater than the rate of the decrease.

B. The first segment of the graph is constant.

C. The second segment of the graph increases at a constant rate.

D. The rate of the decrease is greater than the rate of the increase.

E. The third segment of the graph is decreasing at a constant rate.

Answer:

Given that the graph is linear and it has three parts.

The first part is constant and the second part is increasing at a constant rate and the third part is decreasing at a constant rate. From there options A, B and C are the correct answers.

The rate of the increase is greater than the rate of the decrease.

The first segment of the graph is constant.

The second segment of the graph increases at a constant rate.

**Spiral Review**

Question 8.

Jamie starts a savings account with $75. She deposits $30 in her account monthly. Her friend Carmen’s savings account balance is described by the equation b = 25m + 100, where b is the account balance and m is the number of months. Which account has a greater balance after 6 months?

Answer:

Given that,

Carmen’s savings account balance is described by the equation b = 25m + 100

Where,

b is the account balance

m is the number of months.

After 6 months Carmen’s Saving account balance is b = 25(6) + 100

= 150 + 100

= 250.

Jamie starts a savings account with $75. She deposits $30 in her account monthly.

After 6 months Jamie savings account balance is b = $75 + $30(6)

= $75 + $180

= $255

Jamie’s account has a greater balance after 6 months.

Question 9.

Store A sells two sweatshirts for $25 and seven sweatshirts for $87.50. Store B sells three sweatshirts for $39 and six sweatshirts for $78. Which store has a lower price for one sweatshirt?

Answer:

Given that,

Store A sells two sweatshirts for $25 and seven sweatshirts for $87.50.

Store B sells three sweatshirts for $39 and six sweatshirts for $78.

The cost of each Sweatshirt in store A = $25/2 = 12.5 or $87.50/7 = $12.5

The cost of each Sweatshirt in store B = $39/3 = $13 or $78/6 = $13.

Store A has a lower price for one sweatshirt.