Introduction

Reading Function Values is an important Grade 8 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with reading function values.

What Is Reading Function Values?

Reading Function Values means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Reading Function Values

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: The table below shows values of function \(f\). What is \(f(2)\)?

\(x\)\(0\)\(1\)\(2\)\(3\)
\(f(x)\)\(5\)\(7\)\(9\)\(11\)
  • A. \(7\)
  • B. \(9\)
  • C. \(11\)
  • D. \(5\)

Why it works: Locate \(x=2\) in the table; the corresponding \(f(x)\) value is \(9\).

Answer: \(9\)

Visual Model 2

Question: The graph shows function \(g\). What is \(g(2)\)?

Visual Model 2

  • A. \(2\)
  • B. \(3\)
  • C. \(1\)
  • D. \(4\)

Why it works: Locate \(x=2\) on the horizontal axis and read the corresponding \(y\)-coordinate from the graph: \(y=3\).

Answer: \(3\)

Worked Examples

Example 1

Question: A phone plan charges based on minutes used. The table shows the cost \(C(m)\) for \(m\) minutes. What is \(C(200)\)?

Minutes (\(m\))\(100\)\(200\)\(300\)\(400\)
Cost (\(C(m)\))$\(20\)$\(30\)$\(40\)$\(50\)
  • A. \($20\)
  • B. \($40\)
  • C. \($30\)
  • D. \($50\)
  1. Locate \(m=200\) in the table; the cost is \($30\).

Answer: \($30\)

Example 2

Question: The table shows \(f(x)\). If \(f(x)=8\), what is \(x\)?

\(x\)\(1\)\(2\)\(3\)\(4\)
\(f(x)\)\(4\)\(6\)\(8\)\(10\)
  • A. \(1\)
  • B. \(2\)
  • C. \(3\)
  • D. \(4\)
  1. Find the output value \(8\) in the table; it corresponds to \(x=3\).

Answer: \(3\)

Example 3

Question: The graph shows function \(h\). Which of the following is true?

Example 3

  • A. \(h(2)=3\)
  • B. \(h(1)=1\)
  • C. \(h(3)=2\)
  • D. \(h(4)=3\)
  1. From the graph, at \(x=1\) the point is at \((1,1)\), so \(h(1)=1\).
  2. Options A, C, and D are incorrect based on the plotted points.

Answer: \(h(1)=1\)

Real-World Word Problems

Problem 1

Question: A function \(f\) shows the distance (in miles) from home after \(t\) minutes of driving. Which describes what \(f(20)\) means?

  • A. After driving for 20 miles, you are at some time
  • B. After 20 minutes of driving, you are 20 miles from home
  • C. The distance from home after 20 minutes of driving
  • D. It takes 20 minutes to drive some distance

Why it works: In function notation \(f(20)\), the input is \(t=20\) minutes and the output is the distance. So \(f(20)\) means the distance from home after 20 minutes of driving.

Answer: The distance from home after 20 minutes

Problem 2

Question: The function \(f(x)\) represents postage cost based on weight in ounces: \(f(x)=\begin{cases}0.55 & \text{if } 0 < x \leq 1 \\ 0.75 & \text{if } 1 < x \leq 2 \\ 0.95 & \text{if } 2 < x \leq 3\end{cases}\) What is \(f(1.5)\)?

  • A. \($0.55\)
  • B. \($0.75\)
  • C. \($0.95\)
  • D. \($1.50\)

Why it works: Since \(1 < 1.5 \leq 2\), use the second rule: \(f(1.5)=0.75\). Cost is \($0.75\).

Answer: \($0.75\)

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

Given \(f(x)=2x-5\), what is \(f(4)\)?

  • A. \(11\)
  • B. \(3\)
  • C. \(-1\)
  • D. \(13\)

Question 2

If \(g(x)=x+7\), what is \(g(2)\)?

  • A. \(5\)
  • B. \(9\)
  • C. \(10\)
  • D. \(14\)

Question 3

If \(h(x)=3x\), what is \(h(-2)\)?

  • A. \(-6\)
  • B. \(6\)
  • C. \(-2\)
  • D. \(3\)

Question 4

If \(f(x)=x-3\) and \(f(x)=5\), what is \(x\)?

  • A. \(2\)
  • B. \(8\)
  • C. \(5\)
  • D. \(15\)

Question 5

If \(f(x)=\begin{cases}2x & \text{if } x < 2 \\ 5 & \text{if } x \geq 2\end{cases}\), what is \(f(3)\)?

  • A. \(6\)
  • B. \(3\)
  • C. \(5\)
  • D. \(8\)

Question 6

If \(f(x)=|x-2|\), what is \(f(5)\)?

  • A. \(3\)
  • B. \(-3\)
  • C. \(7\)
  • D. \(-7\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(3\)

Substitute \(x=4\): \(f(4)=2(4)-5=8-5=3\).

Question 2

Answer: \(9\)

Substitute \(x=2\): \(g(2)=2+7=9\).

Question 3

Answer: \(-6\)

Substitute \(x=-2\): \(h(-2)=3(-2)=-6\).

Question 4

Answer: \(8\)

Solve \(x-3=5\) for \(x\): \(x=5+3=8\).

Question 5

Answer: \(5\)

Since \(3 \geq 2\), use the second rule: \(f(3)=5\).

Question 6

Answer: \(3\)

Substitute \(x=5\): \(f(5)=|5-2|=|3|=3\).

Timed practice quizzes

Related Quizzes

After studying Reading Function Values, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 8 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Reading Function Values becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.