Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

or each equation, determine whether its graph is symmetric with respect to the
x-axis, the
y-axis, and the heck all symmetries that apply.
(a)
x^(2)+y+2=0
(b)
y=5x^(3)+2
Symmetry:
Symmetry:

x-axis

x-axis

y-axis

y-axis
origin
origin
none of the above
none of the above

or each equation, determine whether its graph is symmetric with respect to the $x$ -axis, the $y$ -axis, and the heck all symmetries that apply. $\newline$ (a) $x^{2}+y+2=0$ $\newline$ (b) $y=5 x^{3}+2$ $\newline$ Symmetry: $\newline$ Symmetry: $\newline$ $x$ -axis $\newline$ $x$ -axis $\newline$ $y$ -axis $\newline$ $y$ -axis $\newline$ origin $\newline$ origin $\newline$ none of the above $\newline$ none of the above

View step-by-step help

View step-by-step help

Even and odd functions

Full solution

Q. or each equation, determine whether its graph is symmetric with respect to the

x

-axis, the

y

-axis, and the heck all symmetries that apply.

\newline

(a)

x^{2}+y+2=0

\newline

(b)

y=5 x^{3}+2

\newline

Symmetry:

\newline

Symmetry:

\newline

x

-axis

\newline

x

-axis

\newline

y

-axis

\newline

y

-axis

\newline

origin

\newline

origin

\newline

none of the above

\newline

none of the above

Replace $y$ with $-y$ : To determine if the graph of an equation is symmetric with respect to the x-axis, replace $y$ with $-y$ in the equation. If the resulting equation is equivalent to the original, the graph is symmetric with respect to the x-axis. $\newline$ For equation (a) $x^2 + y + 2 = 0$ , replace $y$ with $-y$ to get $x^2 - y + 2 = 0$ . This is not equivalent to the original equation, so the graph is not symmetric with respect to the x-axis.
Replace $x$ with $-x$ : To determine if the graph of an equation is symmetric with respect to the y-axis, replace $x$ with $-x$ in the equation. If the resulting equation is equivalent to the original, the graph is symmetric with respect to the y-axis. $\newline$ For equation (a) $x^2 + y + 2 = 0$ , replace $x$ with $-x$ to get $(-x)^2 + y + 2 = 0$ , which simplifies to $x^2 + y + 2 = 0$ . This is equivalent to the original equation, so the graph is symmetric with respect to the y-axis.
Replace x and y with -x and -y: To determine if the graph of an equation is symmetric with respect to the origin, replace x with -x and y with -y in the equation. If the resulting equation is equivalent to the original, the graph is symmetric with respect to the origin. $\newline$ For equation (a) x^ $2$ + y + $2$ = $0$ , replace x with -x and y with -y to get (-x)^ $2$ - y + $2$ = $0$ , which simplifies to x^ $2$ - y + $2$ = $0$ . This is not equivalent to the original equation, so the graph is not symmetric with respect to the origin.
Repeat for equation (b): Now, we will repeat the process for equation (b) $y = 5x^3 + 2$ . To determine if the graph is symmetric with respect to the $x$ -axis, replace $y$ with $-y$ to get $-y = 5x^3 + 2$ . This is not equivalent to the original equation, so the graph is not symmetric with respect to the $x$ -axis.
Replace $y$ with $-y$ : To determine if the graph is symmetric with respect to the y-axis, replace $x$ with $-x$ to get $y = 5(-x)^3 + 2$ , which simplifies to $y = -5x^3 + 2$ . This is not equivalent to the original equation, so the graph is not symmetric with respect to the y-axis.
Replace $x$ with $-x$ : To determine if the graph is symmetric with respect to the origin, replace $x$ with $-x$ and $y$ with $-y$ to get $-y = 5(-x)^3 + 2$ , which simplifies to $-y = -5x^3 + 2$ . If we multiply both sides by $-1$ , we get $y = 5x^3 - 2$ , which is not equivalent to the original equation, so the graph is not symmetric with respect to the origin.

More problems from Even and odd functions

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 3 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 3 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 3 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 3 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 3 months ago