Algebra 1 Functions and Function Notation Test Solutions and Scoring (PDF)

Algebra 1 math test solutions: Functions and Function Notation – Maths PDF

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This algebra 1 functions test answers for Algebra 1 covers functions and function notation (Common Core F-IF.A.1, F-IF.A.2, F-IF.B.5), with a free PDF to print.

These are worked solutions for the functions test with a scoring guide for every question. Award points for correct method as well as for the final answer. The test totals 20 points, so add the question scores to find the final grade.

Algebra 1 · Common Core State Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5

Algebra 1 functions test answers: worked solutions

Question 1 – Function or not [2 pts]

a) Every input is different, so it is a function.

b) The input 2 has outputs 1 and 4, so it is not a function.

Scoring: 1 point for each correct decision with a reason.

Question 2 – Mapping diagram [2 pts]

Each input has one arrow, so it is a function. The inputs 1 and 2 may share the output 3.

Function; domain $\{1, 2, 4\}$; range $\{3, 6\}$

Scoring: 1 point for the decision; 1 point for the domain and range.

Question 3 – Vertical line test [2 pts]

A vertical line meets the graph twice.

The vertical line $x = 4$ meets the graph at $(4, 2)$ and $(4, -2)$.

Not a function

Scoring: 1 point for the decision; 1 point for the explanation.

Question 4 – Evaluate a function [2 pts]

a) $2(-2)^{2} – 3(-2) + 1 = 8 + 6 + 1 = 15$.

b) $2(3)^{2} – 3(3) + 1 = 18 – 9 + 1 = 10$.

$f(-2) = 15$; $f(3) = 10$

Scoring: 1 point for each correct value.

Question 5 – Input and output [2 pts]

a) $4(6) – 5 = 19$.

b) $4x – 5 = 11$, so $4x = 16$ and $x = 4$.

$f(6) = 19$; $x = 4$

Scoring: 1 point for each part.

Question 6 – Domain and range [2 pts]

Domain: the inputs. Range: the outputs, writing 2 only once.

Domain $\{-1, 0, 1, 4\}$; range $\{-3, 2, 5\}$

Scoring: 1 point for the domain; 1 point for the range.

Question 7 – Phone plan function [3 pts]

a) $20(6) + 15 = 135$.

b) $20m + 15 = 215$, so $20m = 200$ and $m = 10$.

c) Months are counted in whole numbers starting at 0: $m = 0, 1, 2, 3, and so on$.

$135; 10 months; whole numbers $m \ge 0$

Scoring: 1 point per part.

Question 8 – Graph of a segment [3 pts]

The point (1, 2) is on the graph.

a) The x-values run from -2 to 4: $-2 \le x \le 4$.

b) The y-values run from -1 to 5: $-1 \le y \le 5$.

c) The graph passes through $(1, 2)$.

$-2 \le x \le 4$; $-1 \le y \le 5$; 2

Scoring: 1 point per part.

Question 9 – Rule from a table [2 pts]

The outputs increase by 2 each time the input increases by 1, and $f(1) = 3$. So $f(x) = 2x + 1$.

$f(10) = 2(10) + 1 = 21$.

$f(x) = 2x + 1$; $f(10) = 21$

Scoring: 1 point for the rule; 1 point for f(10).

Total score

Total

20 points

Key facts behind this algebra 1 functions test answers

Key facts

A function assigns exactly one output to each input.
The domain is the set of inputs; the range is the set of outputs.
The vertical line test: a graph is a function if no vertical line meets it twice.
f(x) is read “f of x” and means the output when the input is x.
In context, the domain is limited to the inputs that make sense.

How to use this algebra 1 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 Algebra 1 chapters: Algebra 1 math.

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