NBT Mathematics: Functions and Graphs Flashcards

For the parabola y = x² − 6x + 5, which of the following is TRUE?

Answer: The vertex is at (3, −4) and the parabola opens upward

x = −(−6)/(2) = 3; y = 9 − 18 + 5 = −4; positive leading coefficient → opens upward.

If f(x) = 2^x + 1, what is the horizontal asymptote of f?

Answer: y = 1

As x → −∞, 2^x → 0, so f(x) → 1; the horizontal asymptote is y = 1.

The function g(x) = a · b^x passes through (0, 5) and (1, 15). What are a and b?

Answer: a = 5, b = 3

g(0) = a = 5; g(1) = 5b = 15 → b = 3.

The graph of y = f(x) is reflected in the x-axis to give y = g(x). If f(3) = 7, what is g(3)?

Answer: −7

Reflection in the x-axis: g(x) = −f(x), so g(3) = −7.

Which inequality describes the range of f(x) = −2(x + 1)² + 8?

Answer: f(x) ≤ 8

The vertex is maximum at y = 8 (negative a); range is f(x) ≤ 8.

The graph of y = f(x) is shown. Which feature tells you that f is a one-to-one function?

Answer: Every horizontal line cuts the graph at most once

The horizontal line test: if every horizontal line cuts the graph at most once, the function is one-to-one.

The graph shows two functions: f(x) = x² and g(x) = 4x. For x > 0, at which x-value does g(x) exceed f(x)?

Answer: 0 < x < 4

g(x) > f(x) ↔ 4x > x² ↔ 0 0).