Question

1. the graph of a function is shown on the coordinate plane below. between which two values of x is the function linear? and which domain is the graph decreasing? 12. which set of ordered pairs represents a function? a. {(1, 4), (1, 6), (3, 8)} b. {(-2, 5), (0, 5), (2, 5)} c. {(4, -1), (4, 3), (4, 6)} d. {(-3, 2), (-3, -2), (1, 2)} 13. which expression is equivalent to (49x^2 - 9)? a. ((7x - 3)(7x + 3)) b. ((49x - 9)(49x + 9)) c. ((7x - 3)(7x - 3)) d. ((49x - 9)(49x - 9))

Explanation:

Step1: Analyze Q11 (Linear interval)

A linear segment has a constant slope. Looking at the graph, the segment between $x=2$ and $x=5$ is straight (linear).

Step2: Analyze Q11 (Decreasing interval)

A decreasing function has a negative slope (y decreases as x increases). Looking at the graph, the segment between $x=5$ and $x=6$ falls from left to right.

Step3: Analyze Q12 (Function definition)

A function has no repeated x-values in ordered pairs.

• Option A: $x=1$ repeats
• Option B: All x-values ($-2,0,2$) are unique
• Option C: $x=4$ repeats
• Option D: $x=-3$ and $x=1$ repeat

Step4: Analyze Q13 (Difference of squares)

Use the identity $a^2 - b^2=(a-b)(a+b)$. Here, $49x^2=(7x)^2$, $9=3^2$, so $49x^2-9=(7x-3)(7x+3)$.

Answer:

1. Between $x=2$ and $x=5$ the function is linear; Between $x=5$ and $x=6$ the graph is decreasing
2. B. $\{(-2, 5), (0, 5), (2, 5)\}$
3. A. $(7x - 3)(7x + 3)$