Thread: URGENT HELP WITH some problems. :x

1. URGENT HELP WITH some problems. :x

Okay it starts with how to use algebraic tests to check for symmetry with respect to both axes and the origin.

13. y = -4x+1
14. y= 5x-6
15. y=5-x^squared
16.y=x^squared - 10
17. y=x cubed + 3
18. y= -6 -x cubed
19. y = square root of x +5
20. y=|x| +9

And..
I know theres this formula for this its (x-h) squared + (y-k) squared = r squared but
How to find the center of a radius of a circle when they give u just this

21. x squared + y squared = 9
22. x squared + y squared = 4
23. (x+2)squared + y squared = 16
24.x squared + (y-8)squared = 81
25. (x - 1/2) squared + (y + 1)squared = 36
26. (x+4) squared + (y - 3/2)squared = 100

Whoever answers them all first gets thanks IF they helped me understand how to do them correctly
much love
-THANKS

2. If a function is even (i.e. symmetric about the y-axis), then: $f(x) = f(-x)$, i.e. if you plug in -x to your function, you'll get the same function if you plugged in x.

If a function is odd (i.e. symmetric about the origin), then: $f(-x) = -f(x)$, i.e. if you plug in -x to your function, then you'll get the negative of f(x).

Show us your work and we'll point out any errors.

As for the circle, given $(x-a)^2 + (y-b)^2 = r^2$, the centre is given by $(a,b)$ (note the minus signs in front of them in the equation). For example, $(x - 5)^2 + (y + 2)^2 = 9$ has centre $(5, {\color{red}-}2)$

3. Originally Posted by o_O
If a function is even (i.e. symmetric about the y-axis), then: $f(x) = f(-x)$, i.e. if you plug in -x to your function, you'll get the same function if you plugged in x.

If a function is odd (i.e. symmetric about the origin), then: $f(-x) = -f(x)$, i.e. if you plug in -x to your function, then you'll get the negative of f(x).

Show us your work and we'll point out any errors.

As for the circle, given $(x-a)^2 + (y-b)^2 = r^2$, the centre is given by $(a,b)$ (note the minus signs in front of them in the equation). For example, $(x - 5)^2 + (y + 2)^2 = 9$ has centre $(5, {\color{red}-}2)$
Im confused by your first explanation but here if i have say y=-4x + 1
is this function negative or odd? i don't understand.. do i have to plug in (1) to x and see because that is what i understand from your explanations..
or would the function y=5x - 6 be positive because its slope is 5x and its starting point or b is -6?

I am confused in that aspect and if i had something like
y=x cubed + 3 to me this would be positive or am i not correct? if it positive then for me to find out if its symmetric about the origin how would i know this? and if its odd its symmetric about the origin is that what your saying because i get that if its odd its symmetric by the origin and if its even it is symmetric about the y axis but what i also don't understand on something like y=-4x +1 is how i found out what number is odd do i plug in 1 to find out what just y equals and determine if its symmetric about the y axis or origin? So confuseed.
Or do i determine if the slopes odd / or the starting point?

For the 2nd part I understand that something like x squared + y squared = 9
is (x-1)squared + (y - 1) squared = 9 or 3 squared so is that how that is graphed at (-1,-1) and goes 3 to the sides to form the circle on a graph?

and for something like 23. (x+2)squared + y squared = 16 how would i take out (x+2) squared to make it work with the formula square root (x+2) and Square root 16 to get 4 and then subtract 2 and have x + y squared = 2 Sorry if i confused you there. but im completely confused ha.