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Quizzes > High School Quizzes > Technology

Functions and Parameters Practice Quiz

Conquer 5.10.1 with targeted practice questions

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting Function Focus Quiz for high school math students.

Which of the following best describes a function?
A relation where each input has exactly one output
A graph that is symmetric about the y-axis
A set of ordered pairs with no restrictions
A relation where each output has exactly one input
A function is defined as a relation where every input value is paired with exactly one output value. The other options do not satisfy the uniqueness requirement for functions.
Evaluate f(3) for f(x) = 2x + 5.
8
11
10
9
Substituting x = 3 into the function gives 2(3) + 5 = 6 + 5, which equals 11. This simple computation confirms the correct answer.
What is the domain of the function f(x) = √(x - 2)?
x ≥ 2
All real numbers
x > 2
x ≤ 2
Since the square root function requires its argument to be non-negative, we set x - 2 ≥ 0, which results in x ≥ 2. This restriction defines the domain of the function.
Which notation correctly represents the function where the output is the square of the input?
f(x) = 2x
f(x) = x²
f(x) = x + 2
f(x) = √x
The notation f(x) = x² indicates that the function squares the input. The other options describe different operations and do not match the intended definition.
In the linear function f(x) = mx + b, what does the parameter m represent?
The maximum value
The y-intercept
The slope of the line
The function's domain
In the equation of a line, m represents the slope, which indicates the rate at which the line rises or falls. The other options describe different characteristics that m does not represent.
Find f(2) for the function f(x) = 3(x - 1)².
6
1
0
3
Substitute x = 2 into the function: 3(2 - 1)² becomes 3(1)², which simplifies to 3. This direct substitution confirms the correct result.
Which of the following correctly defines the function that multiplies an input by 4 and then subtracts 7?
g(x) = 4(x + 7)
g(x) = 7 - 4x
g(x) = 4(x - 7)
g(x) = 4x - 7
The function that multiplies an input by 4 and then subtracts 7 is represented as g(x) = 4x - 7. The other forms imply different operations or grouping of terms.
If h(x) = 5 - 2x, what is the value of h(-3)?
-1
1
11
-11
Substitute x = -3 into the function: 5 - 2(-3) becomes 5 + 6, which equals 11. Accurate treatment of the negative sign is key to arriving at the correct answer.
Which function among the following has a range of all real numbers?
f(x) = x²
f(x) = 2x + 3
f(x) = √x
f(x) = 1/(x - 2)
A non-constant linear function like f(x) = 2x + 3 will yield every real number as its output, meaning its range is all real numbers. The quadratic and radical functions have restrictions on their ranges.
Given that the linear function f(x) = ax + b passes through (1, 4) and (3, 10), what is the value of a?
4
2
6
3
The slope a can be calculated using the two points: (10 - 4) / (3 - 1) equals 6/2 = 3. Hence, the value of a is 3.
For the quadratic function f(x) = x² - 4x + 3, what are the zeros of the function?
x = 1 and x = 3
x = -1 and x = -3
x = 1 and x = -3
x = -1 and x = 3
Factoring the quadratic equation gives (x - 1)(x - 3) = 0, which results in zeros at x = 1 and x = 3. This method confirms the solution.
If f(x) = |x - 2|, what is the value of f(5)?
-3
2
3
7
Substituting x = 5 into f(x) yields |5 - 2| = |3|, which is 3. The absolute value function ensures the result is non-negative.
Which expression represents the composition (f ∘ g)(x) if f(x) = x + 3 and g(x) = 2x?
x + 6
2x - 3
2(x + 3)
2x + 3
The composition (f ∘ g)(x) means applying f to the result of g(x). Since g(x) = 2x, then f(g(x)) = 2x + 3, which is the correct expression.
What is the inverse of the function f(x) = x - 5?
x + 5
x - 5
5 - x
-x + 5
To find the inverse, swap x and y in the equation y = x - 5 and solve for y, leading to y = x + 5. This shows that the inverse function is f❻¹(x) = x + 5.
Which of the following functions is even?
f(x) = x²
f(x) = x + 1
f(x) = x³
f(x) = x³ + 2
An even function satisfies f(-x) = f(x) for all x, and f(x) = x² clearly meets this condition. The other functions change sign or are not symmetric about the y-axis.
Determine the value of k in the function f(x) = kx - 8 such that f(4) = 0.
4
8
-2
2
Setting f(4) equal to 0 gives the equation 4k - 8 = 0. Solving for k, we find that k must be 2 for the equation to hold true.
For the quadratic function f(x) = ax² + bx + c with vertex at (2, -3), which relationship between the parameters must hold true?
c = -4a
c = 4a
b = -4a
b = 4a
The x-coordinate of the vertex for a quadratic function is given by -b/(2a). Setting -b/(2a) equal to 2 leads to b = -4a, which is the required relationship.
Simplify the function f(x) = (x² - 9)/(x - 3) for all x ≠ 3.
(x + 9)/(x - 3)
x + 3
x - 3
x² + 3
Factor the numerator as (x - 3)(x + 3) and cancel the common factor with the denominator, yielding f(x) = x + 3 for x ≠ 3. This simplification is valid except at x = 3.
If f(x) = 2/(x - 1), what is the effect on the graph when it is transformed to g(x) = f(x + 2)?
Vertical shift up by 2 units
Vertical shift down by 2 units
Horizontal shift right by 2 units
Horizontal shift left by 2 units
Replacing x with x + 2 in the function argument shifts the graph horizontally to the left by 2 units. This type of input modification affects the horizontal placement of the graph.
A piecewise function is defined as f(x) = { x² for x ≤ 0, 2x + 1 for x > 0 }. What is the value of f(0)?
1; because 0 falls in the interval where f(x) = 2x + 1
2; averaging the two parts yields 2
Undefined; the function is ambiguous at x = 0
0; because 0 falls in the interval where f(x) = x²
Since the function specifies f(x) = x² for x ≤ 0 and 0 satisfies this condition, we use the first part. Evaluating f(0) gives 0² = 0, which is the correct answer.
0
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Study Outcomes

  1. Interpret the key components of a function including parameters, domain, and range.
  2. Analyze graphs to determine function behaviors and transformations.
  3. Apply algebraic techniques to evaluate and construct functions based on given conditions.
  4. Assess the impact of parameters on the shape and position of function graphs.
  5. Diagnose common errors in function analysis to enhance problem-solving skills.

5.10.1 Functions & Parameters Cheat Sheet

  1. Functions as Magical Machines - Think of a function as a secret machine that takes an input (x), works its magic, and gives you exactly one output (y). This unique pairing rule means every x you feed in has one and only one y coming out. Ready to slot your numbers into the funnel? Britannica on Functions
  2. Spot the Domain and Range - The domain is like your function's playground (all the x-values it can use), and the range is the set of all outcomes it can spit out (y-values). For example, f(x)=x² lets any real number play but only non-negative results slide down the ramp. AnalyzeMath - Domain & Range
  3. Meet the Parameters - Parameters are the adjustable knobs and dials in your function that stay constant as you play with inputs. In y = mx + b, you twist m to change the slope and set b to shift the line up or down. Britannica on Parameters
  4. Variables vs. Parameters - Variables dance around inside your function, changing value, while parameters stand firm like trusty sidekicks. Understanding this duo helps you predict how your graph will move when you tweak the equation. Math Insight - Variable vs. Parameter
  5. Decode Linear Parameters - In y = 3x + 2, the number 3 is your slope parameter, deciding how steep your route is, and 2 is the y-intercept, marking where you start the journey. Practice swapping these numbers to see how the landscape shifts! OnlineMathLearning - Linear Parameters
  6. Graph Tweaks with Parameter Changes - Tweak parameters in y = ax² + bx + c, and watch how the parabola stretches, shrinks, or slides around the graph paper. It's like adjusting a digital filter to get the perfect picture. Math Insight - Graphing Parameters
  7. Even vs. Odd Functions - Even functions produce mirror images (f(x)=f( - x)) across the y-axis, while odd functions flip around the origin (f( - x)= - f(x)). Spotting symmetry is like finding hidden Easter eggs in your equations. Shiksha - Even and Odd Functions
  8. Master Function Notation - Function notation f(x) = x² + 3x - 5 is your shorthand for saying "plug x into this formula and watch the magic." It keeps your work neat and helps others follow your mathematical masterpiece. OpenStax - Function Notation
  9. Vertical Line Test - Grab a ruler and draw vertical lines across any graph; if a line ever bumps into the curve more than once, you're not looking at a function. It's the ultimate graph detective trick. OpenStax - Vertical Line Test
  10. Real-World Function Fun - Model everyday phenomena like tree growth with h(t) = 20t, where t is time and 20 is your growth rate parameter. These practice stories turn abstract concepts into real-life adventures. Math is Fun - Parameters in Action
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