Function Notation Test Answer Key with Scoring – Algebra 1

Question 1 Is it a function? (2 points)

(a) Each x-value appears once, so each has one output (repeated outputs are fine): function.

(b) The input 0 has outputs 1 and 4: not a function.

Scoring: 1 point per part with a reason.

Question 2 Evaluate a quadratic (2 points)

f(−3) = 9 + 12 + 7 = 28. f(2) = 4 − 8 + 7 = 3.

f(−3) = 28; f(2) = 3

Scoring: 1 point for each value.

Question 3 Vertical line test (2 points)

A vertical line such as x = 3 crosses the circle at (3, 4) and (3, −4), so the input 3 has two outputs.

No, it is not a function.

Scoring: 1 point for the answer, 1 point for naming a vertical line or a repeated input.

Question 4 Interpret function values (3 points)

(a) Six minutes after leaving, the train travels at 48 miles per hour.

(b) Forty minutes after leaving, the train is stopped.

(c) Input: minutes. Output: miles per hour.

Statements interpreted with units

Scoring: 1 point per part.

Question 5 Domain and range of a graph (3 points)

(a) The graph runs from −5 (closed) to 1 (open): −5 ≤ x < 1.

(b) Heights run from −2 (closed) to 4 (open): −2 ≤ y < 4.

(c) The line is y = x + 3, so f(−2.5) = 0.5.

Domain −5 ≤ x < 1; range −2 ≤ y < 4; f(−2.5) = 0.5

Scoring: 1 point per part.

Question 6 Discrete or continuous (2 points)

(a) Tickets are counted in whole numbers 0 to 120, so the domain is discrete.

(b) The outputs are the multiples of 11 from 0 to 1,320: {0, 11, 22, …, 1,320}.

Discrete; range {0, 11, …, 1,320}

Scoring: 1 point per part.

Question 7 Using function notation (3 points)

(a) f(−2) = 6 + 8 = 14.

(b) 6 − 4x = −18, so −4x = −24 and x = 6.

(c) f(x + 1) = 6 − 4(x + 1) = 6 − 4x − 4 = 2 − 4x.

14; x = 6; 2 − 4x

Scoring: 1 point per part.

Question 8 Rental charges (3 points)

(a) R(3.5) = 25 + 42 = 67 dollars.

(b) Domain: 0 ≤ h ≤ 8. At h = 0, R = 25; at h = 8, R = 121. Range: 25 ≤ R ≤ 121.

(c) 25 + 12h = 85, so 12h = 60 and h = 5.

$67; domain 0 ≤ h ≤ 8, range 25 ≤ R ≤ 121; h = 5

Scoring: 1 point per part.