3
x
+
2
y
>
24
3
x
+
2
y
>
24
Solve for
y
y
.
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y
>
−
3
x
2
+
12
y
>
-
3
x
2
+
12
Use the slope-intercept form to find the slope and y-intercept.
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Slope:
−
3
2
-
3
2
Y-Intercept:
12
12
Graph a dashed line, then shade the area above the boundary line since
y
y
is greater than
−
3
x
2
+
12
-
3
x
2
+
12
.
y
>
−
3
x
2
+
12
y
>
-
3
x
2
+
12
48 inches cubed is the answer
The velocity, slope, of a line is always (y2-y1)/(x2-x1), in this case:
slope=(8-2)/(7-9)=6/-2=-3
m=-3
To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.
To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.
<em>Of course, it passes the vertical line test, so its a function. </em>
<em>Does it pass the horizontal line test? </em><em>NO! </em><em>As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places. We therefore eliminate choices A and B. We can eliminate choice C because nowhere is it required a function to pass through the origin for it to be one-to-one. Hence, the answer is D (blue line shows this).</em>
<em>ANSWER: D</em>