SOLUTION: Prove Analytically that f(x)=x^3-4x is odd.
Prove Analytically the f(x)=x^4+2x^2+5 is even.
Write the equation for a function that has a graph with the shape of y=square root
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Question 54753: Prove Analytically that f(x)=x^3-4x is odd.
Prove Analytically the f(x)=x^4+2x^2+5 is even.
Write the equation for a function that has a graph with the shape of y=square root of x, but is reflected in the y-axis and shifted up 12.
Write the equation for a function that has a graph of y=x^2, but is vertically shrunk by a factor of 0.2 and shifted left 15 units.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Prove Analytically that f(x)=x^3-4x is odd.
Substitute -x in for x, if f(-x)=-f(x) then the function is odd.
remember (-1)^(odd#)=-1
Therefore f(-x)=-f(x), so the function is odd.
:
Prove Analytically the f(x)=x^4+2x^2+5 is even.
Substitute -x in for x, if f(-x)=f(x) then the function is even.
remember (-1)^(even#)=1
Therefore f(-x)=f(x), so the function is even.
:
Write the equation for a function that has a graph with the shape of y=square root of x, but is reflected in the y-axis and shifted up 12.
f(-x) results in a reflection about the y-axis.
f(x)+k recults in a vertical shift k units.
Looks like:
reflects about y-axis.
reflects it about y-axis and shiftes the graph up 12 units.
It looks like:
:
Write the equation for a function that has a graph of y=x^2, but is vertically shrunk by a factor of 0.2 and shifted left 15 units.
af(x) results in a vertical shrink if -1
f(x+k) results in a horizontal shift left of k units.
Looks like:
results in a vertical shink of a factor of .2
results in the shrink and the left shift of 15 units.
It looks like:
Happy Calculating!!!
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