Mathematical Reasoning Algebra and Functions Flashcards

Which of the following is a solution to the system of equations? x + y = 7 2x − y = 2

Answer: (3, 4)

For (3, 4): 3 + 4 = 7 ✓ and 2(3) − 4 = 6 − 4 = 2 ✓. Only (3, 4) satisfies both equations.

Factor the expression: x² − 9

Answer: (x + 3)(x − 3)

x² − 9 is a difference of squares: a² − b² = (a + b)(a − b). Here a = x and b = 3, giving (x + 3)(x − 3).

The graph of which equation is a parabola opening downward?

Answer: y = −3x² + 2x − 1

A parabola opens downward when the coefficient of x² is negative. In y = −3x² + 2x − 1, the coefficient is −3 < 0.

What is the slope of the line passing through the points (−2, 3) and (4, −1)?

Answer: −2/3

Slope = (y₂ − y₁)/(x₂ − x₁) = (−1 − 3)/(4 − (−2)) = −4/6 = −2/3.

Solve for x: (x/3) + 2 = 5

Answer: x = 9

Subtract 2: x/3 = 3. Multiply by 3: x = 9.

Which table of values represents a linear function?

Answer: x: 0,1,2,3 → y: 1,3,5,7

In a linear function, y changes by a constant amount for each unit increase in x. In option B, y increases by 2 each time (constant rate of change).