Algebra 2 Functions and Relations Assignment Please complete the following questions to this Algebra 2 assingment. Please make sure you show your work on each problem. Thank you in advance. Functions and Relations

1. Find the equation of the line that is modeled by the values in the table shown below.

x

2

4

6

8

10

12

14

y

1

6

11

16

21

26

31

Part I: Determine the slope of the line. Show the work you did to find the slope. (3 points)

Part II: Using the slope you found in Part I and the values in the table, write the equation of the linear

function represented by the table. Write your equation in point-slope form. (3 points)

2. For each function shown, answer the questions.

Part I: Given the function

,

A. What restriction is there on the value under the square root symbol? In other words, what can’t you

do with a square root expression? (1 point)

B. What is the domain of this function? (2 points)

Part II:

For the system of equations shown below,

A. What are the two slopes of these equations? (1 point)

B. Based on the slopes of the equations, how many solutions does this system have? (1 point)

3. For

, substitute 3 for x in the function to solve for f(3). (2 points)

4. Graph the area bounded by

,

Part I: Graph the area bounded by

points)

and

,

, and

.

. Shade the region that satisfies both inequalities.(4

Part II: To the graph you already produced, add the region bounded by the

lines

and

. Shade the region that satisfies both of these inequalities and the

inequalities from Part I.(6 points)

5. For the function defined by:

Part I: Evaluate

.

A. Identify the function that will be used when x = 0. (1 point)

B. Find the value of this function when x = 0. (1 point)

Part II: Graph

.

A. Graph the first function completely. (1 point)

B. On the same graph you used to answer part (A), graph the second function completely. (1 point)

C. Identify the value of x at which the functions change. Remove the parts of each line that are not

included in domain of the corresponding function. (2 points)

D. Place open and closed circles appropriately on the ends of each line to complete the function.(2

points)

6. Solve the following system of equations algebraically.

Part I: Multiply one of the equations by a constant in order to solve by elimination. Show the new system

of equations below. (2 points)

Part II: Combine the two equations to eliminate one of the variables. Show the result of this combination

below. (2 points)

Part III: Solve for the variable. What is this value? (2 points)

Part IV: Substitute this value back into an equation to solve for the other variable. Write the solution to

this system below. (4 points)

7. Find the solution to the two equations shown below:

Part I: Use these tables of values to graph the two equations. (2 points)

x

0

1

2

y

-9

7

23

x

2

3

4

y

13

9

5

Part II: Based on the graph you drew in Part I, what is the solution to y= 16x 9 and y= -4x + 21? (1

point)

Part III: Both of the equations are written in slope-intercept form. If they are set equal to each other their

solution is the point where they intersect. Find the solution algebraically and show your work. (3 points)

Part IV: How do your answers from Parts II and III compare? Is one more precise than the other?(3

points)

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