Question 1037111: Hi there,
I took a crack at the below questions and this is what I came up with:
Let y = 4 - x2.
(a) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional)
4
(b) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional)
(-2, 2)
(c) Create a table of sample points on the graph of the equation (include at least six points), and use them to help create a graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and attach.)
x y (x, y)
-2 0 (-2,0)
-1 3 (-1, 3)
0 4 (0,4)
1 3 (1, 3)
2 0 (2, 0)
3 -5 (3, -5)
(d) Is the graph symmetric with respect to the x-axis? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
(e) Is the graph symmetric with respect to the y-axis? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
(f) Is the graph symmetric with respect to the origin? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
Any help is very much appreciated! Thank you so much!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I agree with your answers for parts (a), (b), and (c).
For (d), I say NO, because if it were symmetric with respect to the x-axis,
along with point (1,3) the graph should also contain its reflexion across the x-axis (1,-3),
y=4-x^2. expresses y as a function of x,
so for a given x value, such as x=1, there is only one value of y.
For (e), I agree with the YES answer,
because the fact that x appears only squared, as 
meas that y will have the same value for x and -x,
so if the graph contains the point (x,y),
it must also contain the reflexion of (x,y) across the y-axis : the point (-x,y).
For (f), I say NO, because if it were symmetric with respect to the x-axis,
along with point (1,3) the graph should also contain its reflexion across the origin: (-1,-3),
y=4-x^2. expresses y as a function of x,
so for a given x value, such as x=-1, there is only one value of y, y=3.
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