NBT Algebra and Functions Flashcards

Simplify: (x³)² ÷ x⁴

Answer: x²

Apply the power rule: (x³)² = x⁶. Then divide: x⁶ ÷ x⁴ = x⁶⁻⁴ = x². When dividing like bases, subtract exponents.

Which equation represents an exponential function?

Answer: y = 2ˣ

An exponential function has the variable in the exponent position, as in y = 2ˣ. The other options are linear, polynomial, and radical functions respectively.

Solve simultaneously: x + y = 7 and 2x - y = 2

Answer: x = 3, y = 4

Add the two equations: 3x = 9, so x = 3. Substitute back: 3 + y = 7, giving y = 4. The solution is x = 3 and y = 4.

What is the domain of f(x) = 1/(x - 3)?

Answer: All real numbers except x = 3

The function is undefined when the denominator equals zero, i.e., when x - 3 = 0 or x = 3. All other real values of x are valid inputs.

If log₂(x) = 5, what is x?

Answer: 32

By definition, log₂(x) = 5 means 2⁵ = x. Since 2⁵ = 32, we have x = 32. Logarithms and exponents are inverse operations.

What is the y-intercept of y = -2x² + 8x - 6?

Answer: -6

The y-intercept occurs when x = 0. Substituting: y = -2(0)² + 8(0) - 6 = -6. The constant term gives the y-intercept directly.