SOLUTION: a)determine whether the graph 0f 5x^2 -3y=4 is symmetric with respect to the y axis b)determine whether the function f(x)= x^4 +x^2+3 is even odd or neither c)Write an equation f

Question 63101: a)determine whether the graph 0f 5x^2 -3y=4 is symmetric with respect to the y axis
b)determine whether the function f(x)= x^4 +x^2+3 is even odd or neither
c)Write an equation for a function that has a graph with the shape of y=square root of x but shifted to the right 7 units and up 4 units
thank you so much
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
a)determine whether the graph 0f 5x^2 -3y=4 is symmetric with respect to the y axis
If the function is even it's symmetric to the y-axis. We know it's even if we substitute -x in for x and get the same function when you simplify.
5(-x)^2-3y=4
5(-x)(-x)-3y=4
5x^2-3y=4
It's even so it's symmetric to the y-axis.
:
b)determine whether the function f(x)= x^4 +x^2+3 is even odd or neither
If f(-x)=f(x), it's even
If f(-x)=-f(x), it's odd
Otherwise it's neither.
A quick way to check for polynomials is to see if all of the variables' exponents are even, because x^0=1, anything without an variable is even. If this is true, it's even.
If all of the variables have odd exponents, it's odd.
If there's a mixture, it's neither.
f(-x)=(-x)^4+(-x)^2+3
f(-x)=x^4+x^2+3=f(x) It's even.
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c)Write an equation for a function that has a graph with the shape of y=square root of x but shifted to the right 7 units and up 4 units
horizontal shifts happen on the inside of the square root with a sign opposite to the direction of the shift.
Vertical shifts happen outside of the square root with a sign in the direction to the shift.

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Happy Calculating!!!
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