NBT NBT Mathematics: Functions and Graphs 4

Question 1

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

Accepted Answer

x = 2 and x = −4

Answer

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

Question 2

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

Accepted Answer

(3, 7)

Answer

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

Question 3

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

Accepted Answer

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

Answer

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

Question 4

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

Accepted Answer

x = 1, minimum y = −9

Answer

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

Question 5

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

Accepted Answer

f(x) = 4^x

Answer

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

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