Grade 8 · Functions · MAT-08-FN-003
Represent Functions with Tables, Graphs, and Equations
Represent and solve represent functions with tables, graphs, and equations problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve represent functions with tables, graphs, and equations problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify represent functions with tables, graphs, and equations results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Represent Functions with Tables, Graphs, and Equations belongs to functions. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent represent functions with tables, graphs, and equations numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Linear Function Lab
- Model represent functions with tables, graphs, and equations in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
For y=1x+2, find the table value when x=1.
y = 3Table, graph, and equation encode the same relationship.
For y=2x+4, find the table value when x=2.
y = 8Table, graph, and equation encode the same relationship.
For y=3x+6, find the table value when x=3.
y = 15Table, graph, and equation encode the same relationship.
For y=4x+8, find the table value when x=4.
y = 24Table, graph, and equation encode the same relationship.
For y=5x+10, find the table value when x=5.
y = 35Table, graph, and equation encode the same relationship.
For y=6x+3, find the table value when x=6.
y = 39Table, graph, and equation encode the same relationship.
For y=1x+5, find the table value when x=7.
y = 12Table, graph, and equation encode the same relationship.
For y=2x+7, find the table value when x=8.
y = 23Table, graph, and equation encode the same relationship.
For y=3x+9, find the table value when x=1.
y = 12Table, graph, and equation encode the same relationship.
For y=4x+2, find the table value when x=2.
y = 10Table, graph, and equation encode the same relationship.
For y=5x+4, find the table value when x=3.
y = 19Table, graph, and equation encode the same relationship.
For y=6x+6, find the table value when x=4.
y = 30Table, graph, and equation encode the same relationship.
For y=1x+8, find the table value when x=5.
y = 13Table, graph, and equation encode the same relationship.
For y=2x+10, find the table value when x=6.
y = 22Table, graph, and equation encode the same relationship.
For y=3x+3, find the table value when x=7.
y = 24Table, graph, and equation encode the same relationship.
For y=4x+5, find the table value when x=8.
y = 37Table, graph, and equation encode the same relationship.
For y=5x+7, find the table value when x=1.
y = 12Table, graph, and equation encode the same relationship.
For y=6x+9, find the table value when x=2.
y = 21Table, graph, and equation encode the same relationship.
For y=1x+2, find the table value when x=3.
y = 5Table, graph, and equation encode the same relationship.
For y=2x+4, find the table value when x=4.
y = 12Table, graph, and equation encode the same relationship.
Practice
Guided practice with hints
01For y=3x+6, find the table value when x=5.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 21
02For y=4x+8, find the table value when x=6.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 32
03For y=5x+10, find the table value when x=7.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 45
04For y=6x+3, find the table value when x=8.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 51
05For y=1x+5, find the table value when x=1.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 6
06For y=2x+7, find the table value when x=2.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: y = 11
Practice
Independent practice
01For y=3x+9, find the table value when x=3.
Answer: y = 18
02For y=4x+2, find the table value when x=4.
Answer: y = 18
03For y=5x+4, find the table value when x=5.
Answer: y = 29
04For y=6x+6, find the table value when x=6.
Answer: y = 42
05For y=1x+8, find the table value when x=7.
Answer: y = 15
06For y=2x+10, find the table value when x=8.
Answer: y = 26
07For y=3x+3, find the table value when x=1.
Answer: y = 6
08For y=4x+5, find the table value when x=2.
Answer: y = 13
Common mistakes
Learn to catch the error, not just the answer.
Outputs may repeat; one input cannot have two different outputs.
Slope is change per unit; intercept is output at x=0.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Model constant rates and starting values with tables, graphs, and equations.
- Compare functions by rate of change and initial value.
Challenge problems
For y=5x+7, find the table value when x=3.
y = 22
For y=6x+9, find the table value when x=4.
y = 33
For y=1x+2, find the table value when x=5.
y = 7
For y=2x+4, find the table value when x=6.
y = 16
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve represent functions with tables, graphs, and equations problems and justify each result with a valid verification method.
Practice
Mastery check
01For y=3x+6, find the table value when x=7.
Answer: y = 27
02For y=4x+8, find the table value when x=8.
Answer: y = 40
03For y=5x+10, find the table value when x=1.
Answer: y = 15
04For y=6x+3, find the table value when x=2.
Answer: y = 15
05For y=1x+5, find the table value when x=3.
Answer: y = 8
06For y=2x+7, find the table value when x=4.
Answer: y = 15
07For y=3x+9, find the table value when x=5.
Answer: y = 24
08For y=4x+2, find the table value when x=6.
Answer: y = 26
Terminology
Words to know
- function
- A relation assigning exactly one output to each input.
- slope
- Vertical change divided by horizontal change for a nonvertical line.
- y-intercept
- The output where a graph crosses the y-axis.
- rate of change
- Output change per unit input change.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.