8th Grade Understanding Functions Worksheet Solutions (PDF)

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

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This grade 8 functions 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.

This answer key gives a full worked solution for each of the 21 problems on the functions worksheet (Common Core 8.F.A.1, 8.F.A.2 and 8.F.A.3). Compare each step with your own work, not only the final answer, and note any step where your method differed.

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

Grade 8 functions answers: exercises 1 to 10

Exercise 1 – Table function

Each x-value appears once with a single y-value.

Yes, it is a function

Exercise 2 – Repeated input

The input 1 has two outputs, 2 and 3.

No, it is not a function

Exercise 3 – Evaluate

$f(4) = 3 \cdot 4 – 2 = 10$.

$f(4) = 10$

Exercise 4 – Evaluate with a square

$f(-2) = (-2)^{2} + 1 = 4 + 1 = 5$.

$f(-2) = 5$

Exercise 5 – Mapping diagram

Each input has one arrow.

Each input has exactly one arrow. Two inputs (2 and 3) share the output 6, which is allowed.

Yes, it is a function

Exercise 6 – Find the rule

The y-values go up by 2 each time, so $m = 2$. When $x = 0$, $y = 1$, so $b = 1$.

$y = 2x + 1$

Exercise 7 – Graph a function

Table.

Graph of y = x + 2.

Points (0, 2), (1, 3), (2, 4), (3, 5)

Exercise 8 – Compare two functions

A: rate 3, initial value 1. B: rate $5 – 2 = 3$, initial value 2.

Same rate (3); B has the greater initial value (2 versus 1)

Exercise 9 – Graph versus equation

A: rate 2. B: rate $\frac{7 – 1}{2 – 0} = 3$.

Function B has the greater rate (3 versus 2)

Exercise 10 – Linear or nonlinear table

The y-values increase by 3, then 5, then 7. The rate of change is not constant.

Nonlinear

Exercises 11 and up

Exercise 11 – Linear equation

Rewrite as $y = -2x + 5$, which has the form $y = mx + b$.

Linear; rate -2, initial value 5

Exercise 12 – Which are linear

Linear equations have the form $y = mx + b$: (a) and (d). In (b) the variable is squared and in (c) it is in a denominator.

(a) and (d)

Exercise 13 – Domain and range

Inputs: 1, 2, 3. Outputs: 3, 5, 7.

Domain 1, 2, 3; range 3, 5, 7

Exercise 14 – Solve for the input

$4x – 3 = 17$, so $4x = 20$.

$x = 5$

Exercise 15 – Taxi fare function

$f(6) = 2.5 \cdot 6 + 3 = 18$.

2.5 is the cost per mile and 3 is the starting fee.

\$18

Exercise 16 – Is it a function?

Each student has one favorite color, so student to color is a function.

A color can be the favorite of many students, so color to student gives several outputs and is not a function.

Student to color: yes. Color to student: no.

Exercise 17 – Area of a square

$A(5) = 25$ square units.

The graph is a curve and the rate of change is not constant, so it is nonlinear.

25; nonlinear

Exercise 18 – Phone plans

After 4 months: A $= 5 \cdot 4 + 10 = 30$; B $= 28$. B is cheaper.

After 6 months: A $= 40$; B $= 42$. A is cheaper.

Plan B at 4 months; plan A at 6 months

Exercise 19 – Candle

$h = 12 – 1.5t$, linear with rate $-1.5$.

$6 = 12 – 1.5t$, so $t = 4$.

$h = 12 – 1.5t$; linear; after 4 hours

Exercise 20 – Decreasing table

The outputs fall by 2 every time $x$ rises by 2, so the rate is $\frac{-2}{2} = -1$.

$g(x) = -x + 6$.

Linear; rate -1; $g(x) = -x + 6$

Exercise 21 – Explain the vertical line

The input 3 would have many outputs (every point on the line), but a function allows only one output for each input.

It fails the vertical line test

Key facts behind this grade 8 functions 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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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