This grade 8 functions worksheet gives 24 problems on introduction to functions, ordered from easy to hard, with a separate answer key.
These problems practice Common Core standards 8.F.A.1, 8.F.A.2 and 8.F.A.3. Decide whether a table, mapping, graph or equation is a function, evaluate and write function rules, and tell linear from nonlinear. Then compare two functions shown in different ways.
The last seven problems are real-world situations such as rentals, savings and tanks. Work from easiest to hardest and explain each answer in a sentence.
Grade 8 Functions Worksheet: problems 1–5
Problem 1: Function machine
A function machine follows the rule \(y=3x+2\). Find the output for each input: 1, 2, 3 and 4.
Problem 2: Mapping diagram
Does the mapping diagram show a function? Explain.
Problem 3: Two arrows from one input
Does this mapping diagram show a function? Explain.
Problem 4: Repeated input in a table
Is the relation in the table a function? Explain.
Problem 5: Same output every time
The table gives inputs 0, 1, 2, 3 and the output 5 each time. Is it a function?
Grade 8 Functions Worksheet: problems 6–10
Problem 6: Ordered pairs
Decide whether the set of ordered pairs \((1,2)\), \((2,4)\), \((3,6)\), \((4,8)\) is a function. If it is, write the rule.
Problem 7: Points on a graph
The graph shows four points. Is the relation a function? Explain.
Problem 8: Evaluate a function
For \(f(x)=-2x+7\), find \(f(-3)\), \(f(0)\) and \(f(4)\).
Problem 9: Write the rule
Write an equation for the function in the table.
Problem 10: Graph a function
Complete a table for \(y=x-2\) using \(x=-1,0,1,2,3\). Then plot the points and tell what shape they form.
Grade 8 Functions Worksheet: problems 11–15
Problem 11: Linear form
Is \(y=4x-1\) a linear function? Identify \(m\) and \(b\).
Problem 12: Area of a square
The area of a square is \(A=s^{2}\). The figure shows squares with sides 1, 2, 3 and 4. Make a table of side and area. Is the function linear?
Problem 13: Linear or nonlinear tables
Decide whether each table is linear.
- \(x\): 0, 1, 2, 3 and \(y\): 2, 5, 8, 11
- \(x\): 1, 2, 3, 4 and \(y\): 1, 4, 9, 16
Problem 14: Which are linear?
Which of these equations are linear? \(y=5x\), \(y=x^{2}+1\), \(y=7-x\), \(y=\frac{2}{x}\).
Problem 15: Slope and starting value
For \(y=-\frac{1}{2}x+6\), name the rate of change and the initial value, then find the output when \(x=4\).
Grade 8 Functions Worksheet: problems 16–20
Problem 16: Equation versus table
Function A is \(y=2x+3\). Function B is shown in the table. Which function has the greater rate of change? Which has the greater initial value?
Problem 17: Graph versus equation
Function A is graphed through \((0,2)\) and \((2,6)\). Function B is \(y=3x+1\). Compare their rates of change and initial values.
Problem 18: Car rental
A car rental costs a flat fee plus a daily charge. The table shows the cost for 1 to 4 days. Write a rule for the cost \(C\) in terms of days \(d\) and find the cost for 6 days.
Problem 19: Comparing savings
Maya saves with the rule \(M=12+6w\), where \(w\) is weeks. Jamal’s savings are in the table. Who saves money faster, and who has more after 10 weeks?
Problem 20: Garden square
A square garden has side \(s\) feet. Its area is \(A=s^{2}\) and its perimeter is \(P=4s\). Find \(A\) and \(P\) for \(s=3,5,8\). Which function is linear? What happens to each when the side doubles from 3 to 6?
Grade 8 Functions Worksheet: problems 21–24
Problem 21: Homeroom function
Each student has one homeroom, as shown. Is “student to room” a function? Is “room to student” a function? Explain both.
Problem 22: Temperature conversion
The rule \(F=1.8C+32\) converts degrees Celsius to degrees Fahrenheit. Find \(F\) for \(C=0,10,25,100\). Is the function linear?
Problem 23: Falling object
The height in feet of a dropped ball is \(h=100-16t^{2}\) after \(t\) seconds. Find \(h\) for \(t=0,1,2\) and decide whether the function is linear.
Problem 24: Two tanks
Tank A holds \(V=50+4t\) gallons after \(t\) minutes. Tank B is graphed through \((0,20)\) and \((10,80)\). Which tank has more water at 5 minutes, and which fills faster?
How to use this grade 8 functions worksheet
Print this grade 8 functions worksheet as a PDF, solve every problem on paper, then compare with the answer key.
See every chapter on the Grade 8 math page.
