NBT Mathematics: Functions and Graphs Flashcards

The graph of y = 2x − 4 is shifted 3 units upward. What is the new equation?

Answer: y = 2x − 1

Adding 3 to the function: y = 2x − 4 + 3 = 2x − 1.

A table of values shows: x = 0 → y = 1, x = 1 → y = 3, x = 2 → y = 9, x = 3 → y = 27. What is the function?

Answer: y = 3^x

Each y is 3 multiplied by the previous y (×3 ratio), indicating y = 3^x.

The parabola y = x² + bx + 9 has a double root. What is the value of b?

Answer: b = ±6

Double root ↔ discriminant = 0: b² − 4(1)(9) = 0 → b² = 36 → b = ±6.

Which of these functions is ODD (i.e., f(−x) = −f(x))?

Answer: f(x) = x³

f(−x) = (−x)³ = −x³ = −f(x), so x³ is an odd function.

The graph of f(x) is given. From the graph, f(x) > 0 for x ∈ (−∞, −2) ∪ (3, ∞) and f(x) < 0 for x ∈ (−2, 3). What are the roots of f?

Answer: x = −2 and x = 3

The function changes sign at x = −2 and x = 3 — these are the x-intercepts (roots).

For the function f(x) = |x − 2|, what is f(−1)?

Answer: 3

f(−1) = |−1 − 2| = |−3| = 3.

The straight lines y = 2x + 1 and y = 2x − 3 are:

Answer: Parallel

Both lines have gradient 2 but different y-intercepts, so they are parallel.