Question

Which rules define the function graphed below? (15 points cuz I'm stumped)

y=2x+3; y=-1/3x+3
y=2x; y=-1/3x
y=3x+2; y=3x-1
y=-3x+3; y=x+3

Answer 1

Answer:  Choice A

y=2x+3; y=-1/3x+3

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Explanation:

The left portion of the blue curve is y = 2x+3 but it is only graphed when x < 0 (we could argue that $x \le 0$ but I'll set that aside for the other portion).

The right portion is the line y = -1/3x + 3 and it's only graphed when $x \ge 0$

So we could have this piecewise function

$f(x) = \begin{cases}2x+3 \ \text{ if } x < 0\\-\frac{1}{3}x+3 \ \text{ if } x \ge 0\\\end{cases}$

Or we could easily swap the "or equal to" portion to move to the first part instead like this

$f(x) = \begin{cases}2x+3 \ \text{ if } x \le 0\\-\frac{1}{3}x+3 \ \text{ if } x > 0\\\end{cases}$

Either way, we're involving the equations mentioned in choice A