Answer:
C
Step-by-step explanation:
looking at the graph, we see a parabola shifted up 6 units. the function is f(x) = x² + 6
we also see a line with a reflection on the y axis and a vertical shift up 6 units. the function is f(x) = -x + 6
x² + 6 is graphed like a normal parabola (u shaped graph) with an open circle on (3,15). the x coordinate is whats important here, which is 3. we see that there are no values to the right of 3, and only to the left of 3. we can say that the statement x < 3 is true of the parabola, as any value less than 3 is a solution to the parabola.
for -x + 6, we see a line graphed with an closed circle on approximately (3,3). again, the x-coordinate is important here which is 3. the line only goes to the right of 3, meaning the inequality x ≥ 3 is true of the line as any value greater than or equal to 3 is a solution
looking at our answer choices we need to find the following answer:
x² + 6 x < 3 and -x + 6 x ≥ 3
this answer would be C
