NBT NBT Algebra and Functions 5 â Questions and Answers
Question 1: What are the x-intercepts of f(x) = x² â x â 6?
- x = 3 and x = â2 (Correct answer)
- x = â3 and x = 2
- x = 6 and x = â1
- x = 2 and x = 3
Correct answer: x = 3 and x = â2
x² â x â 6 = (x â 3)(x + 2) = 0 gives x = 3 and x = â2.
Question 2: A store sells notebooks for $n each. After a 20% discount, Jess pays $12. What is n?
- $15 (Correct answer)
- $14.40
- $10
- $16
Correct answer: $15
0.80n = 12 â n = 15.
Question 3: If h(x) = â(x â 3), what is the domain of h?
- x ⼠3 (Correct answer)
- x > 3
- x ⼠0
- All real numbers
Correct answer: x ⼠3
The expression under the square root must be non-negative: x â 3 ⼠0, so x ⼠3.
Question 4: The graph of y = f(x) is shifted 4 units left and 2 units down. Which represents the new function?
- y = f(x + 4) â 2 (Correct answer)
- y = f(x â 4) â 2
- y = f(x + 4) + 2
- y = f(x â 4) + 2
Correct answer: y = f(x + 4) â 2
Left shift by 4 replaces x with x + 4; down shift by 2 subtracts 2 from the output.
Question 5: If 2x â y = 7 and x + y = 5, what is the value of x?
- 4 (Correct answer)
- 3
- 1
- 2
Correct answer: 4
Adding the equations gives 3x = 12, so x = 4.
Question 6: What is the inverse of f(x) = (x + 3) / 2?
- fâťÂš(x) = 2x â 3 (Correct answer)
- fâťÂš(x) = 2x + 3
- fâťÂš(x) = (x â 3) / 2
- fâťÂš(x) = (x + 3) / 2
Correct answer: fâťÂš(x) = 2x â 3
Swap x and y: x = (y + 3)/2 â 2x = y + 3 â y = 2x â 3.
Question 7: Which expression is equivalent to (x² â 9) / (x â 3) for x â 3?
- x + 3 (Correct answer)
- x â 3
- x² + 3
- x
Correct answer: x + 3
x² â 9 = (x â 3)(x + 3), so dividing by (x â 3) leaves x + 3.
NBT NBT Algebra and Functions 5
What are the x-intercepts of f(x) = x² â x â 6?