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Quizzes > High School Quizzes > Mathematics

Scientific Notation Practice Quiz

Improve your function and notation skills today

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art themed trivia quiz on function notation for high school math students.

Evaluate f(3) for the function f(x) = 2x + 5.
10
12
11
13
Substitute x = 3 into f(x) = 2x + 5 to get f(3) = 2(3) + 5 = 11. This demonstrates basic evaluation of function notation.
What is the value of f(0) for the function f(x) = 3x - 4?
-3
0
-4
4
By substituting x = 0 into f(x) = 3x - 4, we get f(0) = -4. This problem highlights the effect of the constant term in a linear function.
Express 5000 in proper scientific notation.
5 x 10^2
5 x 10^3
50 x 10^2
0.5 x 10^4
Scientific notation requires a coefficient between 1 and 10 multiplied by a power of 10. For 5000, the correct representation is 5 x 10^3.
Find f(2) for the function f(x) = x^2.
6
2
8
4
Substitute x = 2 into f(x) = x^2 to calculate 2^2 = 4. This confirms the basic evaluation process for a quadratic function.
Determine f(-2) for the function f(x) = 4x - 1.
8
9
-9
7
Plugging x = -2 into f(x) = 4x - 1 gives 4(-2) - 1 = -8 - 1 = -9. This problem illustrates how to handle negative inputs in function evaluation.
Given f(x) = 2x + 3 and g(x) = x^2, what is f(g(2))?
13
6
7
11
First, evaluate g(2) = 2^2 = 4, then substitute into f to get f(4) = 2(4) + 3 = 11. This exercise tests the concept of function composition.
If f(x) = 3x - 5, what is the value of x for which f(x) = 4?
9
4
-3
3
Setting 3x - 5 = 4 and solving gives 3x = 9, so x = 3. This reinforces solving linear equations.
For the function f(x) = x^2 - 2, evaluate f(-3).
7
-8
-7
9
Plugging in x = -3, we calculate (-3)^2 = 9 and then subtract 2 to get 7. This question emphasizes the proper handling of negative numbers in quadratic functions.
Compute f(-1) for f(a) = 2a^3 + a when a = -1.
1
-3
3
-1
Substitute a = -1 into the expression to get 2(-1)^3 + (-1) = -2 - 1 = -3. Accurate use of exponentiation and signs is key in this evaluation.
How is 0.00042 written in scientific notation?
42 x 10^-5
0.42 x 10^-3
4.2 x 10^-4
4.2 x 10^-5
Moving the decimal four places to the right transforms 0.00042 into 4.2, corresponding to a power of 10^-4. This is the correct format for scientific notation.
If f(x) = 5 - x and g(x) = 2x + 1, what is f(g(3))?
2
1
-1
-2
Start by computing g(3) = 2(3) + 1 = 7, and then evaluate f(7) = 5 - 7 = -2. This reinforces the concept of function composition.
Determine the domain of the function f(x) = √(x - 3).
x ≥ 3
all real numbers
x ≤ 3
x > 3
The expression under the square root must be nonnegative, so x - 3 ≥ 0, which means x ≥ 3. This question tests understanding of domain restrictions.
For the function f(x) = x^2 restricted to x ≥ 0, what is its inverse function f❻¹(x)?
-sqrt(x)
sqrt(x)
x^2
x^(1/3)
When f(x) = x^2 and x is restricted to nonnegative values, the inverse function is f❻¹(x) = sqrt(x). This tests the understanding of inverses under domain restrictions.
A linear function is defined as f(x) = cx + 2, and it is given that f(4) = 10. Find the value of c.
4
2
8
3
Substitute x = 4 into the function: 4c + 2 = 10, solving for c gives c = 2. This is a straightforward application of solving a linear equation.
Express (3.1 x 10^2) divided by (1.55 x 10^1) in proper scientific notation.
0.5 x 10^1
2 x 10^2
2 x 10^1
2 x 10^0
Divide the coefficients, 3.1 ÷ 1.55 = 2, and subtract the exponents (2 - 1 = 1) to obtain 2 x 10^1. This operation reinforces the rules of dividing numbers in scientific notation.
Evaluate f(2) for the function f(x) = 2x^2 - 3x + 1.
3
5
4
1
Substitute x = 2 into f(x) to get 2(4) - 3(2) + 1 = 8 - 6 + 1, which equals 3. This reinforces the evaluation of quadratic functions using substitution.
Given f(x) = 10^x, find f(3) and express the result in scientific notation.
1 x 10^2
10^3
1 x 10^3
1000
Calculating f(3) gives 10^3 = 1000, and the proper scientific notation for 1000 is 1 x 10^3. This tests both exponentiation and conversion to scientific notation.
Let h(x) = (f(x))^2 where f(x) = x + 2. Determine h(-2).
4
0
2
-4
First, compute f(-2) = -2 + 2 = 0, and then h(-2) = (0)^2 = 0. This multi-step problem reinforces function composition and subsequent operations.
The function f(x) = ax + b passes through the points (2, 7) and (5, 16). Find the values of a and b.
a = 3, b = 2
a = 4, b = -1
a = 3, b = 1
a = 2, b = 3
Calculate the slope as (16 - 7) / (5 - 2) = 3, and then use one of the points to solve for b, yielding b = 1. This problem consolidates skills in determining the equation of a line from two points.
For the function f(x) = 4x - 8, find the value of x for which f(x) equals its inverse f❻¹(x).
10/3
8/3
4/3
6/3
To find where the function equals its inverse, set f(x) = f❻¹(x) and solve the equation 4x - 8 = (x + 8)/4. Solving this equation yields x = 8/3. This question challenges your understanding of inverse functions.
0
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Study Outcomes

  1. Understand the concept and structure of function notation.
  2. Evaluate functions by substituting given input values.
  3. Analyze and interpret function outputs from algebraic expressions.
  4. Apply function notation to solve practical mathematical problems.
  5. Identify key errors associated with misinterpreting function notation.
  6. Synthesize knowledge of function notation with problem-solving strategies.

Scientific & Function Notation Practice Cheat Sheet

  1. Understand function notation - Think of f(x) as a magic machine: you feed it an input x and it gives you an output f(x). For example, if f(x) = x², then f(3) = 9 because the machine squares whatever you put in. This clean notation keeps your work neat and helps you see how inputs transform into outputs. OpenStax Precalculus: Functions and Function Notation
  2. Practice evaluating functions - Get hands‑on by plugging specific values into the formula and doing the math step by step. For instance, g(x) = 2x + 1 becomes g(5) = 2·5 + 1 = 11, so you really see the process in action. Regular practice turns these steps into second nature and builds your confidence. MathBits Notebook: Function Evaluation Practice
  3. Interpret functions in context - Translate symbols into real‑world stories, like h(t) representing the height of a tossed ball at time t. This helps you connect abstract math to everyday life, making the concepts easier to remember. Imagining scenarios keeps your study sessions fresh and engaging. OpenStax Precalculus: Real‑World Function Notation
  4. Substitute expressions correctly - Remember that f(a + b) means plug (a + b) into the function, not add f(a) and f(b). If f(x) = x², then f(a + b) = (a + b)², which expands to a² + 2ab + b², not a² + b². Mastering this prevents common pitfalls and keeps your solutions error‑free. Online Math Learning: Function Notation Guide
  5. Handle expressions like f(x + h) - When you see f(x + h), you treat (x + h) as a single input and follow the same substitution rules. This skill is especially useful for understanding difference quotients in calculus later on. Practicing with varied expressions builds your problem‑solving muscle. MathBits Notebook: Substitution with Expressions
  6. Appreciate concise relationships - Function notation packs complex relationships between variables into a tidy form, making it easier to manipulate equations. It's like turning a messy paragraph into a clear bullet point. Embrace the power of notation to simplify your math life. OpenStax Precalculus: Function Notation Overview
  7. Identify true functions - Check that each input has exactly one output to confirm a relation is a function. For example, {(1,2), (2,3), (3,4)} is a function because no input repeats with different outputs. Spotting this quickly saves you time on more complex problems. MathBits Notebook: Identifying Functions Practice
  8. Apply notation to various functions - Explore linear, quadratic, and exponential functions to see how notation adapts to each type. Notice how a small change in the formula can completely reshape the graph's behavior. Comparing different families of functions deepens your understanding. OpenStax Algebra & Trigonometry: Functions and Function Notation
  9. Define piecewise functions - Piecewise notation lets you describe one function that behaves differently over separate parts of its domain. You might see f(x) = { x+2 if x<0, 2x if x≥0 }, which tells you exactly how to evaluate at each interval. This is great practice for thinking in "if‑then" math logic. OpenStax Precalculus: Piecewise Functions
  10. Solve equations with function notation - Set f(x) equal to a value and solve for x just like any other equation. For example, if f(x) = x² − 4 and you want f(x) = 0, solve x² − 4 = 0 to get x = ±2. This combines algebra skills with your growing notation fluency. MathBits Notebook: Solving Function Equations
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