Algebra 1
Unit 2 Graphing Linear Equations
2.1 Day 1 Functions and the Coordinate Plane
Mathematician: ________________________________
Period:___________
LEVEL: EMERGING
1) Plot and label the points on the coordinate plane.
2) Write the coordinates of each point.
A (3, 5)
J (-1, -3)
B (-2, 7)
K(
,
)
C (0, -2)
L(
,
)
D (0, 0)
M(
,
)
E (-5, -4)
N(
,
)
F (8, -2)
P(
,
)
G (-7, 1)
R(
,
)
H (5, 0)
S(
,
)
K
L
P
N
M
R
J
S
Directions: List the location of each point as one of the following
Quadrant I (Q1), Quadrant II (Q2), Quadrant III (Q3), Quadrant IV (Q4), Origin, x-axis, or y-axis
3) Point
Location
J
K
4) Point
K
A (3, 5)
L
B (-2, 7)
P
L
M
Location
N
M
D (0, 0)
N
P
C (0, -2)
E (-5, -4)
R
J
R
S
F (8, -2)
G (-7, -1)
S
H (5, 0)
LEVEL: PROFICIENT
Directions: Use the given graph to answer the questions that follow.
5)
6)
What is 𝑓(1)? _______________________
What is 𝑥 if 𝑓(𝑥) = −2? ______________
What is 𝑥 if 𝑓(𝑥) = 4? _______________
What is 𝑥 if 𝑓(𝑥) = 0? _______________
7)
What is 𝑓(0)? _________________________
What is 𝑥 if 𝑓(𝑥) = 2? ________________
Directions: Draw a graph with the given domain and range.
8)
𝐷 = {𝑥 ∈ ℝ|𝑥 = −5}
𝑅 = {𝑦 ∈ ℝ|𝑦 = −4}
9)
𝐷 = {𝑥 ∈ ℝ|𝑥 = 0}
𝑅 = {𝑦 ∈ ℝ|𝑦 = 2}
10)
𝐷 = {𝑥 ∈ ℝ|𝑥 = 5}
𝑅 = {𝑦 ∈ ℝ|𝑦 = 0}
LEVEL: MASTERY
11) Explain what the domain of a
function is, in your own words:
12) Explain what the range of a
function is, in your own words:
Directions: Find the indicated value using the given function.
14) 𝑓(3) given that:
15) 𝑔(−3) given that:
13) What does the “value of a
function” or “function value” refer
to? Explain what f (3) = -5 means.
16) ℎ(10) given that:
1
ℎ(𝑥) = (𝑥 − 13)
4
𝑔(𝑥) = 4𝑥 2 + 2𝑥
𝑓(𝑥) = 2𝑥 − 1
Directions: Identify the domain and range from the given graphs or tables. Write your answer in set notation.
17)
18)
19)
Domain: _____________________________
Domain: _____________________________
Range: _______________________________
Range: _______________________________
20)
𝑥
-3
6
8
𝑦
0
11
-1
21)
𝑥
0
1
5
𝑦
0
3.5
-0.3
Domain: _____________________________
Range: _______________________________
22)
𝑥
-4
-1
0
𝑦
4
0
-1
Domain: _____________________________
Domain: _____________________________
Domain: _____________________________
Range: _______________________________
Range: _______________________________
Range: _______________________________
Algebra 1 Worksheet 2.1 Day 1 Solutions
1.
B
A
D
G
C
H
F
E
2. J (-1, -3), K (0, 9), L (-7, 6), M (-5, 0), N (3, 1), P (9, 4), R (7, -3), S (4, -8)
3. J is in Quadrant III, K is on y-axis, L is in Quadrant II, M is on x-axis, N is in Quadrant I,
P is in Quadrant I, R is in Quadrant IV, S is in Quadrant IV
4. A is in Quadrant I, B is in Quadrant II, C is on y-axis, D is at the Origin, E is in Quadrant III,
F is in Quadrant IV, G is in Quadrant II, H is on x-axis
5. 𝑓(1) = 1 ; 𝑥 = −1
6. 𝑥 = −2 ; 𝑥 = −2
7. 𝑓(0) = −4 ; 𝑥 = −3
8)
9)
10)
11. Answers will vary
12. Answers will vary
13. The value of a function refers to the “Y” value at a particular “X” value. The meaning of 𝑓(3) = −5
is that when x = 3, the function (or y value) is -5.
14. 𝑓(3) = 5
15. 𝑔(−3) = 30
3
16. ℎ(10) = − 4
17. Domain: {𝑥 ∈ ℝ|𝑥 = 4}
Range: {𝑦 ∈ ℝ|𝑦 = 3}
18. Domain: {𝑥 ∈ ℝ|𝑥 = −3}
Range: {𝑦 ∈ ℝ|𝑦 = 2}
19. Domain: {𝑥 ∈ ℝ|𝑥 = 0,3}
Range: {𝑦 ∈ ℝ|𝑦 = −3,2}
20. Domain: {𝑥 ∈ ℝ|𝑥 = −3, 6, 8}
Range: {𝑦 ∈ ℝ|𝑦 = −1, 0, 11}
21. Domain: {𝑥 ∈ ℝ|𝑥 = 0, 1, 5}
Range: {𝑦 ∈ ℝ|𝑦 = −0.3, 0, 3.5}
22. Domain: {𝑥 ∈ ℝ|𝑥 = −4, −1, 0}
Range: {𝑦 ∈ ℝ|𝑦 = −1, 0, 4}