Unit Quiz
Test your mastery of function types, transformations, and applications covered in this unit.
📖 Quiz Instructions
Before You Begin
- Time: Allow 30-40 minutes to complete all questions
- Materials: Paper, pencil, and calculator (graphing calculator recommended)
- Strategy: Answer questions you know first, then return to harder ones
- Scoring: 12 questions total; aim for at least 10 correct (83%)
Topics Covered
- Function families and their properties
- Domain and range
- Transformations (shifts, stretches, reflections)
- Function composition and inverses
- Even and odd functions
- Word problems and applications
✏️ Quiz Questions
Question 1 (Function Identification)
Identify the type of each function:
- f(x) = 4x - 7
- g(x) = x^3 - 2x
- h(x) = 3(2)^x
Show Answer
a) Linear, b) Cubic (polynomial), c) Exponential
Question 2 (Domain and Range)
Find the domain and range of f(x) = sqrt(x + 3) - 2
Show Answer
Domain: x >= -3 (or [-3, infinity))
Range: y >= -2 (or [-2, infinity))
Question 3 (Transformations)
Starting with f(x) = x^2, describe ALL transformations to get g(x) = -3(x + 1)^2 - 4
Show Answer
1. Horizontal shift left 1 unit
2. Vertical stretch by factor of 3
3. Reflection over x-axis
4. Vertical shift down 4 units
Question 4 (Writing Equations)
Write the equation of a function that is the absolute value parent function shifted right 5 units and up 2 units.
Show Answer
f(x) = |x - 5| + 2
Question 5 (Function Composition)
Given f(x) = 2x + 3 and g(x) = x^2 - 1, find:
- f(g(2))
- (g o f)(x)
Show Answer
a) g(2) = 4 - 1 = 3, so f(g(2)) = f(3) = 2(3) + 3 = 9
b) (g o f)(x) = g(f(x)) = g(2x + 3) = (2x + 3)^2 - 1 = 4x^2 + 12x + 9 - 1 = 4x^2 + 12x + 8
Question 6 (Inverse Functions)
Find the inverse of f(x) = (3x - 6)/4
Show Answer
Let y = (3x - 6)/4
Swap: x = (3y - 6)/4
Solve: 4x = 3y - 6
4x + 6 = 3y
y = (4x + 6)/3
f^(-1)(x) = (4x + 6)/3 or (4/3)x + 2
Question 7 (Even/Odd Functions)
Determine whether each function is even, odd, or neither:
- f(x) = x^4 - 3x^2
- g(x) = x^3 + x
- h(x) = x^2 + x
Show Answer
a) f(-x) = x^4 - 3x^2 = f(x), so EVEN
b) g(-x) = -x^3 - x = -(x^3 + x) = -g(x), so ODD
c) h(-x) = x^2 - x, which is neither h(x) nor -h(x), so NEITHER
Question 8 (Graphing)
The vertex of a parabola is at (-2, 5) and it passes through the point (0, 1). Write its equation in vertex form.
Show Answer
Vertex form: y = a(x - h)^2 + k = a(x + 2)^2 + 5
Using point (0, 1): 1 = a(0 + 2)^2 + 5
1 = 4a + 5
-4 = 4a
a = -1
Equation: y = -(x + 2)^2 + 5
Question 9 (Word Problem - Projectile)
A ball is thrown upward with initial velocity 48 ft/s from a height of 4 feet. Its height is given by h(t) = -16t^2 + 48t + 4. Find the maximum height and when it occurs.
Show Answer
Time at max: t = -b/(2a) = -48/(2(-16)) = 48/32 = 1.5 seconds
Max height: h(1.5) = -16(2.25) + 48(1.5) + 4 = -36 + 72 + 4 = 40 feet
Question 10 (Word Problem - Exponential)
A car depreciates 15% per year. If it's worth $25,000 new, write a function V(t) for its value after t years and find its value after 4 years.
Show Answer
V(t) = 25000(0.85)^t (loses 15% means retains 85%)
V(4) = 25000(0.85)^4 = 25000(0.52200625) = $13,050.16
Question 11 (Multiple Transformations)
If f(x) is a function with f(3) = 7, find the point that must be on the graph of g(x) = 2f(x - 4) + 1
Show Answer
For f(x - 4), we need x - 4 = 3, so x = 7
g(7) = 2f(7 - 4) + 1 = 2f(3) + 1 = 2(7) + 1 = 15
The point (7, 15) is on g(x)
Question 12 (Synthesis)
A function f(x) has domain [-3, 5] and range [0, 8]. Find the domain and range of g(x) = -2f(x + 1) + 3
Show Answer
Domain: The shift x + 1 means x + 1 must be in [-3, 5]
So -3 <= x + 1 <= 5, meaning -4 <= x <= 4
Domain of g: [-4, 4]
Range: f outputs [0, 8]
-2f outputs [-16, 0] (flip and stretch)
-2f + 3 outputs [-16 + 3, 0 + 3] = [-13, 3]
Range of g: [-13, 3]
✅ Score Yourself
Scoring Guide
- 12 correct: Excellent! Ready to move on.
- 10-11 correct: Strong understanding. Review missed concepts.
- 8-9 correct: Good foundation. Practice weak areas before continuing.
- 6-7 correct: Review lessons 1-5 and retake quiz.
- Below 6: Return to the beginning of the unit for thorough review.
If You Struggled With...
| Question Type | Review Lesson |
|---|---|
| Function identification (Q1) | Types of Functions |
| Transformations (Q3, Q4, Q11) | Function Transformations |
| Composition/Inverses (Q5, Q6) | Guided Practice |
| Word problems (Q9, Q10) | Word Problems |
| Common errors (Q7, Q12) | Common Mistakes |
🚀 Next Steps
- Record your score and note which topics need more practice
- Review any questions you got wrong
- If you scored well, you're ready for the next unit!
- Consider retaking this quiz in a few days to reinforce retention
Congratulations!
You've completed the Precalculus Introduction unit. The concepts you've learned here - function types, transformations, composition, and inverses - form the foundation for all advanced mathematics. These skills appear frequently on both the SAT and ACT.