Algebra Test Functions and Graphs 2 — Questions and Answers
Question 1: What transformation does y = f(x) + 3 represent?
- Shift 3 units right
- Shift 3 units left
- Shift 3 units up (Correct answer)
- Shift 3 units down
Correct answer: Shift 3 units up
Adding a constant outside the function shifts the graph vertically upward by 3 units.
Question 2: Which function graphs as a straight line?
- f(x) = x²
- f(x) = 2x + 1 (Correct answer)
- f(x) = √x
- f(x) = 1/x
Correct answer: f(x) = 2x + 1
f(x) = 2x + 1 is a linear function and graphs as a straight line.
Question 3: If f(x) = x² + 1 and g(x) = 2x, what is (f ∘ g)(3)?
- 19
- 37 (Correct answer)
- 13
- 7
Correct answer: 37
g(3) = 6; then f(6) = 36 + 1 = 37.
Question 4: A negative leading coefficient on a quadratic function:
- Shifts the parabola up
- Makes it open downward (Correct answer)
- Shifts it right
- Makes it narrower
Correct answer: Makes it open downward
A negative leading coefficient reflects the parabola over the x-axis so it opens downward.
Question 5: What is the inverse of f(x) = 2x + 6?
- f⁻¹(x) = (x - 6)/2 (Correct answer)
- f⁻¹(x) = 2x - 6
- f⁻¹(x) = (x + 6)/2
- f⁻¹(x) = x/2 + 6
Correct answer: f⁻¹(x) = (x - 6)/2
Swap x and y: x = 2y + 6, then solve for y: y = (x - 6)/2.
Question 6: An even function satisfies:
- f(-x) = -f(x)
- f(-x) = f(x) (Correct answer)
- f(x + 1) = f(x)
- f(0) = 0
Correct answer: f(-x) = f(x)
An even function satisfies f(-x) = f(x), meaning it is symmetric about the y-axis.
Algebra Test Functions and Graphs 2
What transformation does y = f(x) + 3 represent?