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Quizzes > High School Quizzes > Mathematics

Identifying and Representing Functions: Practice Quiz

Boost learning with step-by-step answer explanations

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Function Fundamentals Unlocked trivia quiz for high school algebra students.

Which statement best defines a function?
A process that assigns each input many outputs.
A rule that assigns each input exactly one output.
A relationship where outputs do not depend on inputs.
An equation that has no inputs.
A function is a rule that assigns every input exactly one output. This distinguishes functions from general relations where an input might produce multiple outputs.
If f(x) = 2x + 1, what is f(3)?
8
7
6
5
Substitute x = 3 into the function to get f(3) = 2(3) + 1 = 7. This direct substitution confirms the rule of the function.
Which of the following graphs would NOT represent a function?
A parabola opening upward
A linear function with a positive slope
A circle centered at (0,0)
A straight line that passes the vertical line test
A circle fails the vertical line test because many vertical lines intersect it at more than one point. This violates the definition of a function which requires each input to have only one output.
What does the vertical line test determine?
The y-intercept of a graph.
Whether a function is increasing or decreasing.
The slope of a linear function.
Whether a graph represents a function.
The vertical line test is a quick way to check if a graph represents a function. If any vertical line intersects the graph more than once, the graph does not represent a function.
Which notation correctly represents the equation y = 3x as a function?
3x = f
f(3x)
f(x) = 3x
f = 3x
Function notation expresses the relationship by defining the output of a function f for an input x. Here, f(x) = 3x correctly represents the given equation as a function.
Determine the domain of the function f(x) = √(x - 2).
x > 2
x ≤ 2
All real numbers
x ≥ 2
For the square root function to be defined, the radicand must be non-negative. Since x - 2 must be greater than or equal to 0, the domain is x ≥ 2.
Which expression represents the function f(x) = 2(x + 3) after applying the distributive property?
2x - 3
x + 6
2x + 6
2x + 3
Applying the distributive property to 2(x + 3) gives 2x + 6. This shows the function in its expanded form, which is equivalent to the original expression.
Given f(x) = x + 2 and g(x) = 3x, what is the composite function (g ∘ f)(x)?
x + 5
3x - 2
3x + 6
x + 6
The composite function (g ∘ f)(x) means g(f(x)). Substituting f(x) = x + 2 into g gives g(x + 2) = 3(x + 2) = 3x + 6. This is the correctly evaluated composite function.
If h(x) = -x², what is the value of h(-3)?
-9
6
9
-6
Substitute x = -3 into the function to get h(-3) = -(-3)². Since (-3)² is 9, the result is -9. This demonstrates the effect of the negative sign in front of the squared term.
For the function f(x) = |x|, what is f(-5)?
10
5
-5
0
The absolute value function returns the non-negative value of its input. Therefore, f(-5) equals 5, because the absolute value of -5 is 5.
Which option is an example of a piecewise function?
f(x) = x² + 4
f(x) = √x
f(x) = { x + 2 if x < 0; x² if x ≥ 0 }
f(x) = 3x + 1
A piecewise function is defined by different expressions for different intervals of the domain. The provided option clearly assigns one formula for x < 0 and another for x ≥ 0, making it a piecewise function.
Determine the range of the function f(x) = x² for all real x.
f(x) > 0
f(x) ≤ 0
f(x) ≥ 0
All real numbers
Squaring any real number results in a non-negative value. Thus, the outputs of f(x) = x² are always zero or positive, meaning the range is all y such that y ≥ 0.
For the function f(x) = 2x - 4, find the fixed point where f(x) = x.
4
0
2
-4
A fixed point is where the output equals the input. Setting 2x - 4 equal to x and solving gives x = 4, which makes the function's output equal to its input.
Which function represents a horizontal shift of y = x² by 3 units to the right?
y = (x - 3)²
y = x² - 3
y = (x + 3)²
y = x² + 3
A horizontal shift to the right by 3 units is achieved by replacing x with (x - 3) in the function. Hence, y = (x - 3)² correctly represents this transformation.
What does the notation f(3) represent in function terminology?
A function whose variable is 3.
The input value of the function when the output is 3.
The function multiplied by 3.
The output of the function when the input is 3.
f(3) denotes the value obtained by substituting 3 into the function f. It specifically indicates the output corresponding to the input value of 3.
Consider the piecewise function f(x) = { 2x + 1 if x < 0; x² if x ≥ 0 }. What is the value of f(-2)?
-1
-3
5
4
For x = -2, which is less than 0, use the first part of the piecewise function: f(x) = 2x + 1. Substituting gives 2(-2) + 1 = -3, which is the correct value.
For the function f(x) = 1/(x - 5), what is the domain of f?
All real numbers except x = 5
x < 5
All real numbers
x > 5
In the function f(x) = 1/(x - 5), the denominator cannot be zero. Since x - 5 = 0 when x = 5, x = 5 must be excluded from the domain.
If f(x) = (x² - 9)/(x - 3), what is f(3)?
3
Undefined
9
6
Although (x² - 9) factors as (x - 3)(x + 3) and simplifies to x + 3 for x ≠ 3, the original function is undefined at x = 3 due to division by zero. Thus, f(3) is undefined.
Let f(x) = √(2x + 8). For which x does f(x) equal 0?
x = 0
x = 4
x = -4
x = -8
To find when f(x) equals 0, set √(2x + 8) = 0. Squaring both sides gives 2x + 8 = 0, which simplifies to x = -4.
Given the function f(x) = log₂(x - 1), what is its domain?
x < 1
x > 1
x ≥ 1
All real numbers
The logarithm function requires its argument to be positive. For log₂(x - 1) to be defined, x - 1 must be greater than 0, which means x > 1.
0
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Study Outcomes

  1. Understand the definition and notation of functions.
  2. Identify functions using the vertical line test and other criteria.
  3. Represent functions through tables, graphs, and algebraic expressions.
  4. Analyze function behavior by determining domain and range.
  5. Apply key function concepts to solve real-world algebra problems.

Functions Answer Key Cheat Sheet

  1. Definition of a Function - A function is a relation where each input value maps to exactly one output, like a vending machine that gives you one snack per button press. No button (input) can ever produce two different snacks (outputs). Identify Functions Worksheet, Meaning, and Examples
  2. Vertical Line Test - If you can draw a vertical line that hits a graph more than once, you know it's not a function. It's a quick visual trick that keeps you from mixing up graph buddies! Identifying and Representing Functions
  3. Function Representations - Functions can wear many costumes: tables, graphs, mappings, or equations, each revealing a different side of the story. Switching between these views helps you spot patterns and solve problems like a math detective. Different Ways of Representing Functions
  4. Function Notation - When you see f(x), read it as "function of x" - it's the output you get when you feed x into the rule. For example, if f(x) = 2x + 3, plugging in x = 2 gives f(2) = 7, like following a recipe for math cookies. Function Notation and Evaluation Practice
  5. Common Function Types - Linear (f(x) = mx + b), quadratic (f(x) = ax² + bx + c), and absolute value (f(x) = |x|) are your math friends that show up everywhere - from line graphs to parabolas to V-shapes. Recognizing these families helps you predict behavior and sketch graphs in a snap. Summary: Characteristics of Functions and Their Graphs
  6. Domain vs. Range - The domain is the set of all inputs you're allowed to use, while the range is all the outputs you can get. For example, with f(x) = √x, you can only plug in x ≥ 0, so your domain starts at zero and your range follows suit. Identifying and Representing Functions
  7. Evaluating Functions - To evaluate a function, just substitute your chosen input into the rule and simplify to find the output. For instance, if g(x) = x² - 4, plugging in 3 gives g(3) = 9 - 4 = 5, like plugging an ingredient into a recipe to see what you cook up. The Definition of a Function (Practice Problems)
  8. One-to-One Functions - A one-to-one function pairs each input with a unique output and vice versa, meaning no horizontal line will ever touch its graph twice. These are crucial for finding inverses and keeping your math reversible. Summary: Characteristics of Functions and Their Graphs
  9. Ordered Pair Check - When given a set of ordered pairs, make sure no x-value appears more than once with different y-values. For example, {(1,2), (2,3), (1,4)} fails the function test, but {(1,2), (2,3), (3,4)} passes with flying colors. The Definition of a Function (Practice Problems)
  10. Graph Transformations - Shifts, reflections, stretches, and compressions are like dress-up options for your parent function, moving and tweaking its graph. Mastering these moves means you can sketch any transformed function without breaking a sweat. Summary: Characteristics of Functions and Their Graphs
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