The graph of y^2=x^2 is symmetric with respect to which axis? a. x-axis c. both b. y-axis d. neither
2 answers:
Answer:
c. both
Step-by-step explanation:
Given equation is
Now we need to check if the graph of is symmetric with respect to which axis?
a. x-axis c. both b. y-axis d. neither
We know that if f(-x) reflect the graph about y-axis
so let's change x by -x into given function to see if that equation remains unchanged or not
That is same as previous equation.
<u>Hence given graph is symmetric about y-axis.</u>
We know that if -f(x) reflect the graph about x-axis
so let's change y by -y into given function to see if that equation remains unchanged or not
That is same as previous equation.
<u>Hence given graph is symmetric about x-axis.</u>
So the correct choice is c. both
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Answer:
maximum difference is 38 at x = -3
Step-by-step explanation:
This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.
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Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.
h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2
Then the derivative is ...
h'(x) = 3x² +4x -15 = (x +3)(3x -5)
This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.
The maximum difference between f(x) and g(x) is 38 at x = -3.
