L82 - A1 - 3.5 - RW Function Notation & Comparing Functions

Labeling

Complete the table for the given function:

$$f\left(x\right)=-\frac{1}{2}x-1$$

Drag labels to their correct position on the image

0

-5

1

3

2

-1

-4

-3

-2

Graphing

Graph the given function:

$$f\left(x\right)=-\frac{1}{2}x-1$$

Dropdown

Match the following answers for the function:

$$f\left(x\right)=-\frac{1}{2}x-1$$

Domain -

Select answer

Range -

Select answer

X-intercept -​ ​

Select answer

y-intercept - ​

Select answer

Slope -​

Select answer

​Vocabulary

Categorize

Options (12)

Range

Output

$$f\left(x\right)$$  

Dependent

Slope

Rate of Change

$$\frac{rise}{run}$$  

Domain

Input

Independent

y-intercept

Total

Match the vocabulary terms to the correct variable for Slope Intercept Form

$$y=mx+b$$

y

m

x

b

Math Response

1. A submarine starts at a depth of 50 meters below sea level and descends at a constant rate. The total depth, , in meters, is a linear function of the number of minutes, , that the submarine has been descending. The function is given by:

$$D(t)=50+10t$$

If the submarine has been descending for 8 minutes, what is its depth?

Type answer here

Correct Answer: 130

Deg^°

Rad

Math Response

2. An airplane starts at an altitude of 1,000 meters and climbs at a constant rate. The total altitude, , in meters, is a linear function of the number of minutes, , that the airplane has been climbing. The function is given by:

$$A(t)=1000+150t$$

If the airplane has been climbing for 6 minutes, what is its altitude?

Type answer here

Correct Answer: 1900

Deg^°

Rad

Math Response

3. Jasmine is saving money to buy a concert ticket. She already has $5 and plans to save $4 each day.

The function  $$J(x)=4x+5$$  represents the total amount of money Jasmine has after  days.

How many days will it take Jasmine to save $29?

Type answer here

Correct Answer: 6

Deg^°

Rad

Math Response

4. Marcus wants to buy a new video game. He already has $12 and plans to save $3 each day.

The function  $$M(x)=3x+12$$ represents the total amount of money Marcus has after  days.

How many days will it take Marcus to save $30?

Type answer here

Correct Answer: 6

Deg^°

Rad

Multiple Choice

5. An amusement park charges $6 per person for a ride. Each ride car can hold a maximum of 4 people. The total cost, C(x), in dollars, can be modeled by the function $$C(x)=6x$$ .

Which of the following is the appropriate range in this context?

• {0, 1, 2, 3, 4}

• 0 ≤ y ≤ 4

• {0, 6, 12, 18, 24}

• 0 ≤ y ≤ 24

Multiple Choice

6. A pizza shop charges $10 per pizza. You’re hosting a party and plan to spend up to $60. The total cost, P(x), in dollars, can be modeled by the function   $$P(x)=10x$$ where x is the number of pizzas ordered.

Which of the following is the appropriate domain in this context?

• 0 ≤ y ≤ 60

• {0, 10, 20, 30, 40, 50, 60}

• 0 ≤ x ≤ 6

• {0, 1, 2, 3, 4, 5, 6}

Multiple Choice

7. Given the function $$f(x)=4x+1$$  and the graph of g(x) shown on the right, which function f(x)  or g(x) has the greater slope?

• f(x)

• g(x)

• They have the same slope

• Cannot be determined.

Multiple Choice

7. Given the function $$f(x)=2x+1$$  and the graph of g(x) shown on the right, which function f(x)  or g(x) has the greater slope?

• f(x)

• g(x)

• They have the same slope

• Cannot be determined.

Multiple Choice

9. The graphs of two linear functions, f(x) and g(x), are shown below. Compare the key features of the two functions. Which of the following statements is true?

• Both functions have the same slope but different y-intercepts

• Function f(x) has a greater slope than g(x), but they have the same y-intercept.

• Function g(x) has a greater y-intercept and a greater slope than f(x).

• The functions have different slopes and different y-intercepts.

Multiple Choice

10. The graphs of two linear functions,  and , are shown below. Compare the key features of the two functions. Which of the following statements is true?

• Both functions have the same slope but different y-intercepts

• Function f(x) has a greater slope than g(x), but they have the same y-intercept.

• Function g(x) has a greater y-intercept and a greater slope than f(x).

• The functions have different slopes and different y-intercepts.

​Complete your Notes Quiz