NBT Algebra and Functions Flashcards

What are the x-intercepts of f(x) = x² − x − 6?

Answer: x = 3 and x = −2

x² − x − 6 = (x − 3)(x + 2) = 0 gives x = 3 and x = −2.

A store sells notebooks for $n each. After a 20% discount, Jess pays $12. What is n?

Answer: $15

0.80n = 12 → n = 15.

If h(x) = √(x − 3), what is the domain of h?

Answer: x ≥ 3

The expression under the square root must be non-negative: x − 3 ≥ 0, so x ≥ 3.

The graph of y = f(x) is shifted 4 units left and 2 units down. Which represents the new function?

Answer: y = f(x + 4) − 2

Left shift by 4 replaces x with x + 4; down shift by 2 subtracts 2 from the output.

If 2x − y = 7 and x + y = 5, what is the value of x?

Answer: 4

Adding the equations gives 3x = 12, so x = 4.

What is the inverse of f(x) = (x + 3) / 2?

Answer: f⁻¹(x) = 2x − 3

Swap x and y: x = (y + 3)/2 → 2x = y + 3 → y = 2x − 3.

Which expression is equivalent to (x² − 9) / (x − 3) for x ≠ 3?

Answer: x + 3

x² − 9 = (x − 3)(x + 3), so dividing by (x − 3) leaves x + 3.