Keystone Test Algebra: Functions and Data 2 — Questions and Answers
Question 1: A function is defined as f(x) = 3x² - 2x + 1. What is f(-2)?
- 9
- 17 (Correct answer)
- 13
- 5
Correct answer: 17
f(-2) = 3(-2)² - 2(-2) + 1 = 3(4) + 4 + 1 = 12 + 4 + 1 = 17.
Question 2: Which scatter plot description indicates a strong negative correlation?
- Points cluster tightly along a line going up to the right
- Points are randomly scattered with no pattern
- Points cluster tightly along a line going down to the right (Correct answer)
- Points form a curve opening upward
Correct answer: Points cluster tightly along a line going down to the right
A strong negative correlation means as x increases, y decreases, shown by points tightly clustered along a downward-sloping line.
Question 3: The table shows: x = {1, 2, 3, 4} and y = {5, 8, 11, 14}. Which function models this data?
- y = 2x + 3
- y = 3x + 2 (Correct answer)
- y = x + 4
- y = 4x + 1
Correct answer: y = 3x + 2
The common difference is 3 (slope), and when x=1, y=5: 3(1)+2=5, confirming y = 3x + 2.
Question 4: If g(x) = 2x - 5, for what value of x does g(x) = 0?
- x = 5
- x = 2.5 (Correct answer)
- x = -5
- x = 10
Correct answer: x = 2.5
Set 2x - 5 = 0, so 2x = 5, giving x = 2.5.
Question 5: A data set has values: 4, 7, 7, 9, 13. What is the mean of this data set?
- 7
- 8 (Correct answer)
- 9
- 10
Correct answer: 8
Mean = (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8.
Question 6: Which of the following represents a function?
- A circle centered at the origin
- {(1,2),(1,3),(2,4)}
- {(1,2),(2,3),(3,4)} (Correct answer)
- x = 4 (a vertical line)
Correct answer: {(1,2),(2,3),(3,4)}
A function requires each x-value to map to exactly one y-value; only {(1,2),(2,3),(3,4)} satisfies this.
Question 7: The function f(x) = -x² + 4 has a maximum value. What is that maximum value?
- 0
- 2
- 4 (Correct answer)
- -4
Correct answer: 4
The parabola opens downward; its vertex is at (0, 4), so the maximum value is 4.
Keystone Test Algebra: Functions and Data 2
A function is defined as f(x) = 3x² - 2x + 1.
What is f(-2)?