Answer:
A, y = {x²+ 6 x < 3
{-x + 6 x ≥ 3
Step-by-step explanation:
the parabola (the u shaped graph or the graph that is on top) is expressed by the function x² + 6, as it is 6 units up from the origin (0,0)
the line is expressed by the function -x + 6, as its first reflected across the x axis from the origin (0,0) and is then shifted 6 units up
these functions on this graph represent a piecewise function
looking at x² + 6, we see that it has an open circle on (3, 15). this means that the x coordinate 3 is not included in the solution to the function, and any x values that would be included are less than 3. in an inequality, this is expressed as x < 3
looking at our answer choices, this matches answer A. but let me continue with the explanation in case you run into a question that doesnt have it that easy
when we look at -x + 6, we see that it has a closed circle on (3,4) (approx (3,4), not sure about y-coordinate but its still the same). a closed circle means that the x coordinate 3 is included in the solution, and any numbers <em>greater than 3</em> are included in the solution. as an inequality, this is expressed as x ≥ 3
again we look at our answer choices and see that A is the only choice that supports both of these functions, so A is our answer
