## Engage NY Eureka Math Algebra 1 Module 3 Lesson 11 Answer Key

### Eureka Math Algebra 1 Module 3 Lesson 11 Exercise Answer Key

Exercise 1.

Perform the instructions in the following programming code as if you were a computer and your paper were the computer screen.

Declare x integer

For all x from 2 to 8

Print 2x + 3

Next x

Answer:

7

9

11

13

15

17

19

Exercise 2.

We can also build a set by appending ordered pairs. Perform the instructions in the following programming code as if you were a computer and your paper were the computer screen (the first few are done for you).

Declare x integer

Initialize G as {}

For all x from 2 to 8

Append (x, 2x + 3) to G

Next x

Print G

Output:

{(2, 7), (3, 9), __________________________________________}

Answer:

{(2, 7), (3, 9), (4, 11), (5, 13), (6, 15), (7, 17), (8, 19)}

Exercise 3.

Plot the function f on the Cartesian plane using the following for-next thought code.

Declare x real

Let f(x) = x^{2} + 1

Initialize G as {}

For all x such that -2 ≤ x ≤ 3

Append (x, f(x) ) to G

Next x

Plot G

Answer:

b. For each step of the for-next loop, what is the input value?

Answer:

The number x

c. For each step of the for-next loop, what is the output value?

Answer:

f(x) or the value of x^{2} + 1

d. What is the domain of the function f?

Answer:

The interval -2 ≤ x ≤ 3

e. What is the range of the function f?

Answer:

The interval 1 ≤ f(x) ≤ 10 for all x in the domain

### Eureka Math Algebra 1 Module 3 Lesson 11 Problem Set Answer Key

Question 1.

Perform the instructions for each of the following programming codes as if you were a computer and your paper were the computer screen.

Declare x integer

For all x from 0 to 4

Print 2x

Next x

Answer:

0, 2, 4, 6, 8

(Note that if replicating a computer the numbers would be printed vertically, as shown below.)

0

2

4

6

8

b.

Declare x integer

For all x from 0 to 10

Print 2x + 1

Next x

Answer:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21

c.

Declare x integer

For all x from 2 to 8

Print x^{2}

Next x

Answer:

4, 9, 16, 25, 36, 49, 64

d.

Declare x integer

For all x from 0 to 4

Print 10∙3^{x}

Next x

Answer:

10, 30, 90, 270, 810

Question 2.

Perform the instructions for each of the following programming codes as if you were a computer and your paper were the computer screen.

a.

Declare x integer

Let f(x) = (x + 1)(x – 1) – x^{2}

Initialize G as {}

For all x from -3 to 3

Append (x, f(x)) to G

Next x

Plot G

Answer:

b.

Declare x integer

Let f(x) = 3^{-x}

Initialize G as {}

For all x from -3 to 3

Append (x, f(x)) to G

Next x

Plot G

Answer:

c.

Declare x real

Let f(x) = x^{3}

Initialize G as {}

For all x such that -2 ≤ x ≤ 2

Append (x, f(x)) to G

Next x

Plot G

Answer:

Question 3.

Answer the following questions about the thought code:

Declare x real

Let f(x) = (x – 2)(x – 4)

Initialize G as {}

For all x such that 0 ≤ x ≤ 5

Append (x, f(x)) to G

Next x

Plot G

a. What is the domain of the function f?

Answer:

0 ≤ x ≤ 5

b. Plot the graph of f according to the instructions in the thought code.

Answer:

c. Look at your graph of f. What is the range of f?

Answer:

-1 ≤ f(x) ≤ 8 for all x in the domain.

d. Write three or four sentences describing in words how the thought code works.

Answer:

First, the domain of the variable x is stated as the real numbers, the formula for f is given, and the set G is initialized with nothing in it. Then the for-next loop goes through each number between 0 and 5 inclusive and appends the point (x, f(x)) to the set G. After every point is appended to G, the graph of f is plotted on the Cartesian plane.

Question 4.

Sketch the graph of the functions defined by the following formulas, and write the graph of f as a set using set-builder notation. (Hint: Assume the domain is all real numbers unless specified in the problem.)

a. f(x) = x + 2

Answer:

Graph of f = {(x, x + 2) | x real}

b. f(x) = 3x + 2

Answer:

Graph of f = {(x, 3x + 2) | x real}

c. f(x) = 3x – 2

Answer:

Graph of f = {(x, 3x – 2) | x real}

d. f(x) = -3x-2

Answer:

Graph of f = {(x, -3x – 2) | x real}

e. f(x) = -3x + 2

Answer:

Graph of f = {(x, -3x + 2) | x real}

f. f(x) = –\(\frac{1}{3}\) x + 2, -3 ≤ x ≤ 3

Answer:

Graph of f = {(x, –\(\frac{1}{3}\) x + 2) | x real, -3 ≤ x ≤ 3} or Graph of f = {(x, –\(\frac{1}{3}\) x + 2) |-3 ≤ x ≤ 3}

g. f(x) = (x + 1)^{2 }– x^{2}, -2 ≤ x ≤ 5

Answer:

Graph of f = {(x, (x + 1)^{2 }– x^{2} ) | x real, -2 ≤ x ≤ 5}

OR

Graph of f = {(x, (x + 1)^{2 }– x^{2} ) |-2 ≤ x ≤ 5}

h. f(x) = (x + 1)^{2 }– (x – 1)^{2}, -2 ≤ x ≤ 4

Answer:

Graph of f = {(x, (x + 1)^{2}-(x-1)^{2} ) | x real, -2 ≤ x ≤ 4}

OR

Graph of f = {(x, (x + 1)^{2}-(x-1)^{2} ) |-2 ≤ x ≤ 4}

Question 5.

The figure shows the graph of f(x) = -5x + c.

a. Find the value of c.

Answer:

c = 7

b. If the graph of f intersects the x-axis at B, find the coordinates of B.

Answer:

B(\(\frac{7}{5}\), 0)

Question 6.

The figure shows the graph of f(x) = \(\frac{1}{2}\) x + c.

a. Find the value of c.

Answer:

c = 3

b. If the graph of f intersects the y-axis at B, find the coordinates of B.

Answer:

B(0, 3)

c. Find the area of triangle AOB.

Answer:

9 square units

### Eureka Math Algebra 1 Module 3 Lesson 11 Exit Ticket Answer Key

Question 1.

Perform the instructions for the following programming code as if you were a computer and your paper were the computer screen.

Declare x integer

Let f(x) = 2x + 1

Initialize G as {}

For all x from -3 to 2

Append (x, f(x)) to G

Next x

Plot G

Answer:

Question 2.

Write three or four sentences describing in words how the thought code works.

Answer:

The first three lines declare the domain of the variable x to be the integers, specifies the formula for f, and sets G to be the empty set with no points in it. Then the for-next loop goes through each integer between -3 and 2 inclusive and appends the point (x, f(x)) to the set G. After every point is appended to G, the graph of f is plotted on the Cartesian plane.