MoGEA Test Functions, Patterns, and Algebraic Relationships 3

Question 1

For the piecewise function f(x) = {x + 2 if x < 0; x² if x ≥ 0}, what is f(-3)?

Accepted Answer

-1

Answer

Since -3 < 0, use the rule x + 2: f(-3) = -3 + 2 = -1.

Question 2

How does the graph of f(x) = (x - 3)² + 2 compare to the graph of f(x) = x²?

Accepted Answer

Shifted 3 units right and 2 units up

Answer

Replacing x with (x - 3) shifts the graph right 3 units, and adding 2 shifts it up 2 units.

Question 3

If y varies directly with x, and y = 12 when x = 4, what is the constant of variation?

Accepted Answer

3

Answer

For direct variation y = kx, the constant k = y / x = 12 / 4 = 3.

Question 4

If y varies inversely with x, and y = 6 when x = 4, what is y when x = 8?

Accepted Answer

3

Answer

The constant k = xy = 24; when x = 8, y = 24 / 8 = 3.

Question 5

A sequence is defined recursively as a₁ = 5 and aₙ = aₙ₋₁ + 4. What is a₄?

Accepted Answer

17

Answer

a₁=5, a₂=9, a₃=13, a₄=13+4=17.

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