NBT Mathematics: Functions and Graphs Flashcards

The graph of a parabola has roots at x = −3 and x = 5 and a y-intercept of −15. What is the leading coefficient a?

Answer: 1

y = a(x+3)(x−5); at x=0: a(3)(−5) = −15 → −15a = −15 → a = 1.

Which graph has the SAME shape as y = x² but opens downward?

Answer: y = −x²

Multiplying by −1 reflects the parabola in the x-axis, making it open downward.

A graph shows an exponential function passing through (0, 1) and (1, 4). What is the base of the exponential function?

Answer: 4

f(x) = b^x; f(0) = 1 ✓; f(1) = b = 4, so the base is 4.

For f(x) = x² − 4, find the values of x for which f(x) = 0.

Answer: x = ±2

x² − 4 = 0 → x² = 4 → x = ±2.

The line y = 2x + 3 intersects the parabola y = x² at two points. What are the x-coordinates of the intersections?

Answer: x = −1 and x = 3

Set x² = 2x + 3 → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0 → x = 3 or x = −1.

A function is described as 'many-to-one'. Which example illustrates this?

Answer: f(x) = x² (both x = 2 and x = −2 give f = 4)

f(x) = x² maps both 2 and −2 to 4, making it many-to-one.

The domain of f(x) is restricted to {−2, 0, 2, 4}. If f(x) = 3x − 1, what is the range?

Answer: {−7, −1, 5, 11}

f(−2) = −7, f(0) = −1, f(2) = 5, f(4) = 11.