MoGEA Test Functions, Patterns, and Algebraic Relationships 2 — Questions and Answers
Question 1: If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
- 13
- 19 (Correct answer)
- 25
- 49
Correct answer: 19
First evaluate g(3) = 9, then f(9) = 2(9) + 1 = 19.
Question 2: What is the inverse function of f(x) = 3x - 6?
- f⁻¹(x) = (x + 6) / 3 (Correct answer)
- f⁻¹(x) = (x - 6) / 3
- f⁻¹(x) = 3x + 6
- f⁻¹(x) = x / 3 - 6
Correct answer: f⁻¹(x) = (x + 6) / 3
Swap x and y: x = 3y - 6, then solve for y: y = (x + 6) / 3.
Question 3: Which statement best describes the behavior of f(x) = 2ˣ as x increases?
- The function decreases at a constant rate
- The function increases at a constant rate
- The function increases at an increasing rate (Correct answer)
- The function decreases at a decreasing rate
Correct answer: The function increases at an increasing rate
Exponential growth functions like 2ˣ increase at an accelerating (increasing) rate, not a constant one.
Question 4: What are the x-intercepts of f(x) = x² - 5x + 6?
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = 1 and x = 6
- x = -1 and x = 6
Correct answer: x = 2 and x = 3
Factoring gives (x - 2)(x - 3) = 0, so x = 2 and x = 3.
Question 5: A table shows inputs 1, 2, 3, 4 with outputs 5, 8, 11, 14. Which rule describes this pattern?
- y = 2x + 3
- y = 3x + 2 (Correct answer)
- y = 4x + 1
- y = 5x
Correct answer: y = 3x + 2
Testing y = 3x + 2: 3(1)+2=5, 3(2)+2=8, 3(3)+2=11, 3(4)+2=14 — all match.
Question 6: A savings account starts with $100 and earns $15 per week. Which function represents the total amount after w weeks?
- A(w) = 100 + 15
- A(w) = 100w
- A(w) = 15w + 100 (Correct answer)
- A(w) = 115w
Correct answer: A(w) = 15w + 100
The total equals the initial $100 plus $15 multiplied by the number of weeks: A(w) = 15w + 100.
Question 7: Which statement is true about f(x) = 2x + 3 and g(x) = 2x - 1?
- They have the same y-intercept
- They have the same slope (Correct answer)
- They intersect at x = 0
- They have the same x-intercept
Correct answer: They have the same slope
Both functions have a coefficient of 2 for x, so they share the same slope of 2 and are parallel.
MoGEA Test Functions, Patterns, and Algebraic Relationships 2
If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?