NBT Mathematics: Functions and Graphs Flashcards

The equation of a parabola is y = −(x + 1)² + 9. What are the x-intercepts?

Answer: x = 2 and x = −4

Set y = 0: (x + 1)² = 9 → x + 1 = ±3 → x = 2 or x = −4.

f(x) = 3x − 2 and g(x) = x + 4. Where do f and g intersect?

Answer: (3, 7)

Set 3x − 2 = x + 4 → 2x = 6 → x = 3; y = 3+4 = 7. Point: (3, 7).

The graph of y = (1/2)^x compared to y = 2^x is:

Answer: A reflection of y = 2^x in the y-axis

(1/2)^x = 2^(−x), which is y = 2^x reflected in the y-axis.

The function f(x) = x² − 2x − 8 has a minimum value at:

Answer: x = 1, minimum y = −9

Axis: x = 1; f(1) = 1 − 2 − 8 = −9. Minimum is (1, −9).

A graph of f(x) is increasing for all x. Which could be f(x)?

Answer: f(x) = 4^x

4^x is an exponential function with base > 1, which always increases.

The graph y = x² is translated 4 units to the right. What is the new equation?

Answer: y = (x − 4)²

A horizontal shift right by 4 replaces x with (x − 4): y = (x − 4)².

A straight line graph passes through A(−2, 4) and B(4, 1). What is its gradient?

Answer: −1/2

m = (1 − 4) ÷ (4 − (−2)) = −3 ÷ 6 = −1/2.