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Quizzes > Mathematics

Functions Unit Test: 20-Question Practice Quiz

Quick algebra functions practice quiz with instant results.

Editorial: Review CompletedCreated By: Ernesto MelgarUpdated Aug 27, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Function Mastery Challenge, a dynamic math quiz for high school students.

This 20-question quiz helps you check your skills for a functions unit test and find gaps fast. Get quick feedback on notation, graphs, and composition, with tips for review. For targeted practice, try the function notation quiz, build fluency with graphing functions practice, or sharpen skills with the composition of functions quiz.

Which of the following best defines a function?
A rule that assigns exactly one output to each input
A set of ordered pairs with no specific rule
A relation that assigns multiple outputs for some inputs
A mathematical operation that always returns the same number
A function assigns exactly one output to every input, which is the defining property checked by the vertical line test. This distinguishes functions from more general relations.
If f(x) = 3x + 2, what is f(4)?
14
12
10
16
By substituting 4 into the function, f(4) becomes 3(4) + 2 which equals 12 + 2 = 14. This demonstrates simple evaluation of a linear function.
Determine if the relation {(1, 2), (1, 3), (2, 4)} is a function.
Yes, because it has a rule
No, because the outputs are not in order
Yes, because it contains ordered pairs
No, because an input leads to two different outputs
A function requires every input to have a single unique output. In this relation, the input value 1 is related to both 2 and 3, violating the definition of a function.
What is the domain of the function f(x) = x²?
Only positive numbers
All real numbers
Only non-negative numbers
Only integers
The function f(x) = x² is defined for every real number because any real number can be squared. Therefore, the domain of f(x) is all real numbers.
Which graph characteristic confirms that a graph represents a function?
Passing the vertical line test
Passing the horizontal line test
Being symmetrical about the y-axis
Being a closed curve
A graph represents a function if no vertical line intersects it more than once. This vertical line test ensures that every input corresponds to only one output.
If f(x) = x² - 1, what is f(3)?
9
6
7
8
Substituting 3 into the function gives f(3) = 3² - 1 = 9 - 1, which equals 8. This problem reinforces basic substitution in a quadratic expression.
Given the function g(x) = 2x - 5, solve for x when g(x) = 3.
1
4
3
5
Setting 2x - 5 equal to 3, we add 5 to get 2x = 8 and then divide by 2 to find x = 4. This illustrates solving simple linear equations.
What is the inverse of the function h(x) = x + 7?
x - 7
x + 7
-x - 7
7 - x
To find the inverse, swap the variables in y = x + 7 to get x = y + 7 and then solve for y, yielding y = x - 7. This process demonstrates the concept of function inversion.
Determine the range of the function f(x) = x² for all real numbers.
All non-negative real numbers
All real numbers
Only whole numbers
All positive real numbers
Since squaring any real number always gives a result that is zero or positive, the range of f(x) = x² is all non-negative real numbers. This is a key property of quadratic functions.
Which method is used to determine if a graph represents a function?
Horizontal line test
Vertical line test
Slope analysis
Y-intercept identification
The vertical line test checks if any vertical line intersects the graph more than once, which is the condition for a relation to be a function. This method is fundamental when analyzing graphs of functions.
If f(x) = 4x - 1, what is f(0)?
4
0
1
-1
Substituting 0 into the function gives f(0) = 4(0) - 1 which equals -1. This is a basic example of evaluating a function at a specific point.
Given f(x) = 2x + 3, what is the value of f(-2)?
2
-1
-2
1
By substituting -2 into f(x) = 2x + 3, we compute f(-2) = 2(-2) + 3 = -4 + 3, which equals -1. This question reinforces the impact of negative inputs on linear functions.
Which of the following represents a linear function?
2x + 5
3x³ - 2
1/x + 4
x² + 3
A linear function has the form f(x) = mx + b, and 2x + 5 fits this format perfectly. The other options represent quadratic, cubic, or reciprocal functions.
What is the value of f(2) if f(x) = x² + 2x + 1?
8
9
6
7
Substituting 2 into the function gives f(2) = 2² + 2(2) + 1 = 4 + 4 + 1, which equals 9. This demonstrates evaluating a quadratic function using substitution.
If f(x) = x² + 3x + 2, what are the x-intercepts of the function?
x = 1 and x = 2
x = -2 only
x = -1 and x = -2
x = -1 only
Factoring the quadratic yields (x + 1)(x + 2) = 0, so the solutions are x = -1 and x = -2. These x-intercepts are the points where the graph crosses the x-axis.
Given the piecewise function f(x) = { x + 2 if x < 0; x² if x ≥ 0 }, what is f(-3)?
-1
-5
5
1
For values of x less than 0, the function is defined as f(x) = x + 2. Substituting -3 yields f(-3) = -3 + 2 = -1, which is the correct evaluation.
For the function f(x) = (x - 4)(x + 2), what are the x-intercepts?
x = 4 only
x = -4 and x = 2
x = -2 and x = 4
x = -2 only
Setting each factor equal to zero gives x - 4 = 0 and x + 2 = 0, which result in x = 4 and x = -2 respectively. These are the points where the graph intersects the x-axis.
For the function f(x) = 3x² - 2x + 5, calculate f(1) - f(-1).
0
-4
6
4
Evaluating the function gives f(1) = 3(1)² - 2(1) + 5 = 6 and f(-1) = 3(1) + 2 + 5 = 10. Their difference, f(1) - f(-1), is 6 - 10 = -4.
Consider the composite function (f ∘ g)(x) where f(x) = 2x + 1 and g(x) = x². What is (f ∘ g)(3)?
9
7
19
13
First, compute g(3) = 3² = 9, then substitute into f to obtain f(9) = 2(9) + 1 = 19. This problem demonstrates the process of evaluating composite functions.
Which transformation does the graph of f(x) = (x - 3)² + 2 represent compared to the basic graph of f(x) = x²?
Shifted 3 units right and 2 units downward
Shifted 3 units left and 2 units upward
Shifted 3 units left and 2 units downward
Shifted 3 units right and 2 units upward
The expression (x - 3)² indicates a horizontal shift of 3 units to the right, while the +2 indicates a vertical shift upward by 2 units. This correctly describes the transformation from the basic parabola y = x².
0
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Study Outcomes

  1. Analyze the behavior of functions through graph interpretation.
  2. Apply different transformation techniques to modify function graphs.
  3. Evaluate functions for specific inputs using substitution methods.
  4. Explain the components of a function including domain and range.
  5. Compare various types of functions and their characteristics.

Functions Unit Test Answers Cheat Sheet

  1. Understanding Functions - Functions are like magical machines that turn each input into a single output - no duplicates allowed! Think of f(x)=x²: each x you plug in yields one unique y every time. Mastering this concept is your first step to function fame.
  2. Vertical Line Test - Want to know if a graph is a function in a snap? Drag an imaginary vertical line across it - if it ever crosses more than once, that graph is out of the function club! This quick trick ensures you keep only one y for each x.
  3. Domain and Range - The domain is your input playground (all possible x's), and the range is where outputs (y's) get to roam. For f(x)=√x, only x ≥ 0 can join the party, and y ≥ 0 is where the fun happens. Knowing these boundaries helps you avoid math mishaps.
  4. Linear Functions - Straight-line superstars follow f(x)=mx+b, where m is the slope (steepness) and b is the y-intercept (where it meets the y-axis). For example, f(x)=2x+3 climbs two units up for every one unit right and starts at 3 on the y-axis. They're the simplest mapping out there - perfect for building confidence!
  5. Identifying Function Types - Spot the genre! Linear (f(x)=mx+b) are your straight-line hits; quadratic (f(x)=ax²+bx+c) bring the dramatic parabolas; exponential (f(x)=a·bˣ) skyrocket or dive. Recognizing each type helps you anticipate graph shapes and behaviors like a pro.
  6. Inverse Functions - Inverses flip the script by swapping inputs and outputs. To find one, swap x and y in the equation and solve for y. So f(x)=2x+3 becomes f❻¹(x)=(x - 3)/2 - reverse engineering math style!
  7. Function Composition - Think of composition as a two-step dance: g(x) goes first, then f(x) takes the stage. If f(x)=x+1 and g(x)=2x, f(g(x))=2x+1 - smooth moves all the way through! It's like chaining math operations together for double the fun.
  8. Transformations of Functions - Shifts, stretches, and reflections let you remix graphs like a DJ. f(x)+k jumps up by k, f(x - h) slides right by h, and -f(x) flips it upside-down. Master these moves to sketch any function in seconds.
  9. One-to-One Functions - A one-to-one function is a perfect pairing - each y hooks up with only one x. The horizontal line test seals the deal: if any horizontal line crosses more than once, it's not one-to-one. Ideal for when you need safe inverses!
  10. Arithmetic & Geometric Sequences - Sequences are functions in disguise! Arithmetic sequences add a constant difference each time (think +3, +3, +3), while geometric sequences multiply by a constant ratio (×2, ×2, ×2). Spotting these patterns makes sequence problems a breeze.
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