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Quizzes > High School Quizzes > Mathematics

Properties of Functions: Level H Practice Quiz

Master function concepts with engaging practice tests

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on algebraic functions and exponent rules for high school students.

What is the value of the function f(x)=2x+3 when x=4?
9
11
10
12
By substituting x = 4 into f(x) = 2x + 3, we compute 2(4) + 3 which equals 11. The other options result from miscalculations.
Which of the following statements best describes a function?
Each input value corresponds to exactly one output value.
Every output value must have a unique input.
The same input can yield different outputs on repeated evaluations.
An output value can be linked to multiple input values.
A function assigns exactly one output to every input, which is the definition used in mathematics. The other choices either reverse this idea or state properties that do not define a function.
What is the domain of the function f(x)=√x?
x ≥ 0
All real numbers
x > 0
x ≤ 0
The square root function is defined only for non-negative numbers, meaning that x must be greater than or equal to zero. The other options either exclude zero or include negative values.
What is the value of 5^0?
Undefined
0
5
1
Any non-zero number raised to the power of zero is equal to 1. The other options demonstrate common misunderstandings of this exponent rule.
Which exponent property is correctly applied in simplifying a^m * a^n?
a^(m+n)
a^(m-n)
a^(m*n)
a^(n/m)
When multiplying like bases, the exponents are added together, so a^m * a^n simplifies to a^(m+n). The other options incorrectly apply the rules of exponents.
Simplify the expression (2^3)^2.
16
64
8
512
Using the power rule (a^b)^c = a^(b*c), we have (2^3)^2 = 2^(3*2) = 2^6, which equals 64. The other options are the result of misapplying the exponent rules.
Simplify the expression: (x^2 * x^3) / x^4.
x^5
x^0
x
x^2
Multiply by adding exponents in the numerator: x^2 * x^3 = x^(2+3) = x^5, and then subtract the exponent in the denominator: x^(5-4) = x. The other options are outcomes of incorrect exponent operations.
Which property is used to simplify the expression a^m / a^n?
a^(m-n)
a^(n-m)
a^(m+n)
a^(m*n)
When dividing powers with the same base, the exponent in the denominator is subtracted from the exponent in the numerator, resulting in a^(m-n). The other options do not correctly represent this rule.
If f(x) = 3x - 2, what is the value of f(5)?
15
17
8
13
By substituting x = 5 into the function f(x) = 3x - 2, we get f(5) = 3(5) - 2 = 15 - 2 = 13. The other options arise from simple arithmetic errors.
Express the radical √(a^3) in exponential form.
a^(1/2)
a^(2/3)
a^(3/2)
a^3
The radical √(a^3) can be written as (a^3)^(1/2), which simplifies to a^(3/2) using the rule for exponents. The other answers are results of common mistakes when converting roots to fractional exponents.
Given g(x) = x^2 and h(x) = 2x + 1, what is the value of the composite function (g ∘ h)(2)?
25
9
5
15
First, compute h(2) = 2(2) + 1 = 5, then apply g: g(5) = 5^2 = 25. The other values result from errors in the composition or calculation of the functions.
Simplify the expression (3^4) * (3^-6).
9
3^2
1/9
3^10
Using the rule for multiplying powers with the same base, add the exponents: 3^(4 + (-6)) = 3^(-2), which is equal to 1/(3^2) or 1/9. The incorrect options stem from miscalculations of the exponent operation.
Simplify the expression (-x)^2.
-x^2
2x
x^2
-2x
Squaring a negative number removes the negative sign, so (-x)^2 equals x^2. The other options do not correctly apply the rule for squaring negative expressions.
Evaluate 2^3 * 4^2 by expressing all terms with base 2.
128
256
64
32
Since 4 can be written as 2^2, 4^2 becomes (2^2)^2 = 2^4. Then 2^3 * 2^4 = 2^(3+4) = 2^7, which equals 128. The alternative options reflect incorrect exponent addition or conversion.
What is the inverse function of f(x) = 2x + 5?
(x-5)/2
(5-x)/2
(x+5)/2
2x-5
To find the inverse, swap x and y in the equation y = 2x + 5 to get x = 2y + 5, and then solve for y: y = (x-5)/2. The other options result from incorrect manipulation of the equation.
Given the function f(x) = (x^2 - 4)/(x - 2) for x ≠ 2, simplify f(x) and determine f(3).
5
6
3
7
Factor the numerator as (x - 2)(x + 2), which cancels with the denominator (x - 2), leaving f(x) = x + 2. Substituting x = 3 gives 3 + 2 = 5.
Solve for x in the equation 2^(x+1) = 16.
4
2
3
5
Since 16 is 2^4, setting the exponents equal gives x + 1 = 4, so x = 3. The other answers do not satisfy the equation when the bases are equal.
Find the inverse function of f(x) = (3x - 1)/(2x + 5).
(3-2x)/(5x+1)
(-1-5x)/(2x-3)
(5x+1)/(3-2x)
(-5x-1)/(3-2x)
To find the inverse, replace f(x) with y, swap x and y to get x = (3y - 1)/(2y + 5), and solve for y. The correct rearrangement yields the inverse function y = (-1 - 5x)/(2x - 3).
Rewrite the expression 2^-3 * x^-2 using positive exponents.
8/(x^2)
8x^2
1/(8x^2)
1/(2^3) + x^-2
Apply the rule for negative exponents: 2^-3 becomes 1/2^3 (which is 1/8) and x^-2 becomes 1/x^2. Multiplying these gives 1/(8x^2). The other options reflect errors in rewriting the expression.
Consider the piecewise function f(x) defined by f(x) = { x^2 if x < b, 3x + 1 if x ≥ b }. For f(x) to be continuous at x = b, what must be the value of b?
b = 3
b = (3 + √13)/2
b = (3 ± √13)/2
b = 2
Continuity at x = b requires that the left-hand limit equal the right-hand value, so set x^2 = 3x + 1 when x = b. Solving the equation b^2 - 3b - 1 = 0 yields b = (3 ± √13)/2, which is the complete solution.
0
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Study Outcomes

  1. Understand the fundamental properties of algebraic functions.
  2. Analyze and interpret function behavior through exponent rules.
  3. Apply exponent rules to simplify and manipulate algebraic expressions.
  4. Evaluate learned concepts through practice problems to build test confidence.
  5. Synthesize algebraic function concepts to solve real-world problems.

Properties of Functions Quiz - Level H Cheat Sheet

  1. Master the Product Rule - When you multiply expressions with the same base, you add their exponents. For instance, x^2 × x^3 = x^(2+3) = x^5. Think of it like stacking power‑up blocks for a bigger boost! Dive into the Product Rule
  2. Understand the Quotient Rule - Dividing like bases means you subtract the exponents. For example, x^5 / x^2 = x^(5−2) = x^3. Imagine sharing pizza slices and seeing what's left - subtract to simplify! Explore the Quotient Rule
  3. Apply the Power Rule - When raising a power to another power, multiply the exponents. For example, (x^2)^3 = x^(2×3) = x^6. It's like turbocharging your engine for exponential acceleration! Unlock the Power Rule
  4. Zero Exponent Rule - Any non‑zero base raised to the zero power equals 1. For instance, 5^0 = 1 and x^0 = 1. Think of it as hitting the reset button that always gives you one! Master the Zero Exponent
  5. Negative Exponent Rule - A negative exponent flips the base into its reciprocal: a^(−n) = 1/a^n. For example, x^(−3) = 1/x^3. It's like turning the fraction inside‑out for a fresh perspective! Discover Negative Exponents
  6. Power of a Product Rule - Distribute the exponent across each factor: (ab)^n = a^n × b^n. For example, (2x)^3 = 2^3 × x^3 = 8x^3. Share the exponent love with all parts of the product! Try the Product Power Trick
  7. Power of a Quotient Rule - Apply the exponent to both numerator and denominator: (a/b)^n = a^n / b^n. For instance, (x/y)^2 = x^2 / y^2. Divide and conquer by powering up both sides equally! Conquer the Quotient Power
  8. Simplify with Multiple Rules - Combine exponent rules step by step for complex expressions. For example, (x^3)^2 / x^4 = x^6 / x^4 = x^2. It's like solving a puzzle - apply each rule in order! Tackle Complex Simplifications
  9. Practice with Real Numbers - Plug in actual numbers to see rules in action and build confidence. For example, 2^3 × 2^4 = 2^7 = 128. Crunching real values makes the theory click! Level Up with Number Practice
  10. Engage with Interactive Exercises - Test your skills with quizzes and challenges that reinforce learning. Interactive problems make studying far more fun and memorable. Jump into Interactive Exercises
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