8th Grade Understanding Functions Test with Point Values (PDF)

8th Grade math test: Understanding Functions – Maths PDF

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This grade 8 functions test for 8th Grade covers understanding functions (Common Core 8.F.A.1, 8.F.A.2, 8.F.A.3), with a free PDF to print.

This 20-point test checks functions, function notation, linear and nonlinear functions and comparing functions (Common Core 8.F.A.1, 8.F.A.2 and 8.F.A.3). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Understanding Functions
Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3
Time: 45 minutes
Total: 20 points

Grade 8 functions test: questions

Question 1 – Function or not [3 pts]

Relation 1.

Does the mapping diagram show a function? Explain. Then change one arrow so that it does.

Question 2 – Evaluate [2 pts]

Find $f(5)$ if $f(x) = 4x – 7$. (1 point)
Find $g(-3)$ if $g(x) = x^{2} – 4$. (1 point)

Question 3 – Write a rule [3 pts]

Write a rule for the table and find $y$ when $x = 10$.

Question 4 – Linear or nonlinear [3 pts]

A graph.

Is the graphed function linear? Give two reasons.

Question 5 – Compare [3 pts]

Function A.

Function A is graphed. Function B is $y = 5x – 1$. Which has the greater rate of change? Which has the greater initial value?

Question 6 – Function in context [2 pts]

A skating rink charges \$5 for skate rental plus \$3 per hour. Write a function for the cost $c$ after $h$ hours and find the cost for 4 hours.

Question 7 – Domain and range [2 pts]

A function has the ordered pairs (0, 4), (1, 6), (2, 8). Write its inputs and outputs, then write its rule.

Question 8 – Explain [2 pts]

Mei says $y = 3$ is not a function because every input gives the same output. Is she right?

Key facts behind this grade 8 functions test

Key facts

Every input has exactly one output in a function.
Function notation: $f(x) = 2x + 1$ means $f(3) = 7$.
Vertical line test: a graph is a function only if no vertical line touches it twice.
Linear functions have a constant rate of change and graph as straight lines.
Compare functions using rate of change and initial value, whatever their representation.

How to use this grade 8 functions test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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