8th Grade Understanding Functions Test Solutions and Scoring (PDF)

8th Grade math test solutions: Understanding Functions – Maths PDF

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This grade 8 functions test answers 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.

Use this answer key to score the functions test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3

Grade 8 functions test answers: worked solutions

Question 1 – Function or not [3 pts]

A fixed version.

No: the input 2 has two outputs, 7 and 9. Removing the arrow from 2 to 9 gives a function.

Scoring: 1 point for no, 1 point for the reason, 1 point for a correct fix.

Question 2 – Evaluate [2 pts]

$4 \cdot 5 – 7 = 13$
$(-3)^{2} – 4 = 5$

Scoring: 1 point each.

Question 3 – Write a rule [3 pts]

Graph of y = 3x + 4.

Rate 3, initial value 4: $y = 3x + 4$.

When $x = 10$: $y = 34$.

Scoring: 1 point for the rate, 1 point for the rule, 1 point for 34.

Question 4 – Linear or nonlinear [3 pts]

It is nonlinear: the graph is a curve rather than a straight line, and the rate of change between (1, 1) and (3, 9) is 4 but it is smaller between earlier points.

Scoring: 1 point for nonlinear, 1 point for each reason.

Question 5 – Compare [3 pts]

A: rate 2, initial 3. B: rate 5, initial -1.

B has the greater rate; A has the greater initial value

Scoring: 1 point for each rate and initial value correctly found, 1 point for the comparisons.

Question 6 – Function in context [2 pts]

$c = 3h + 5$; $c(4) = 17$.

Scoring: 1 point for the rule. 1 point for \$17.

Question 7 – Domain and range [2 pts]

Inputs 0, 1, 2; outputs 4, 6, 8. Rule: $y = 2x + 4$.

Scoring: 1 point for the lists. 1 point for the rule.

Question 8 – Explain [2 pts]

No. A function only requires one output per input. Here each input has the single output 3.

Scoring: 1 point for no. 1 point for the reason.

Total score

Total

20 points

Key facts behind this grade 8 functions test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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