# how would this equation look:

y=f(x+3)

when y=f(x)= x^2

would it look like so....

x^2(x+3)

adam, there's a slight problem with your notation in the expression y = f(x+3). Ordinarily we wouldn't put an expression in place of a variable, unless we were making what is termed a composite function. I'm not sure if this is what you meant. Your second expression, y=f(x)=x^2, is a valid expression for a second degree equation. Your last expression is not correct for this function.
Let me make a guess at what the question is asking: Does it state that if you are given y=f(x)=x^2 , what is the value for f(x) when x=3?
If that is the question, then they want to know what y is when you substitute 3 for x. The response would be when x=3, y=f(3) and you would use the equation for f(x), which is x^2, to find y. If this isn't the question, write back.

No. If f(x)=x^2
then f(x+3)=(x+3)^2
the composite of F(x+3) on f(x) is (x+3)^2

Ok, then you are doing a composite function. You have f = x^2 and g = x+3 as functions of x and you want f o g.
Then f(g(x)) = (x+3)^2 as you have.
I wasn't sure in the first post what you were asking for.

When I am subtract or adding, multiplying or dividing number how do i know if it is positive or negative

-4(2x - 3) = -8x + 5

Tammy, the solution to this is simplify it.

-4(2x - 3) = -8x + 5
-8x + 12 = -8x + 5 add 8x to both sides..
12=5
which is impossible, so the original statement of
-4(2x - 3) = -8x + 5
is not possible.

9 months ago

## It seems there was a mistake in the simplification of the equation. Let's go through it again step by step.

To determine if a number is positive or negative when adding, subtracting, multiplying, or dividing, you need to consider the signs involved.

- If two numbers have the same sign (both positive or both negative), you add their absolute values and keep the common sign.
- If two numbers have different signs, you subtract their absolute values and keep the sign of the number with the larger absolute value.

For multiplication and division:
- If two numbers have the same sign, the result is positive.
- If two numbers have different signs, the result is negative.

Now let's solve the equation -4(2x - 3) = -8x + 5 correctly:

Start by distributing -4 to the expression inside the parentheses:
-4(2x - 3) = -8x + 5
-8x + 12 = -8x + 5

Here you can see that the -8x term cancels out on both sides. So, we are left with:
12 = 5

This is a contradiction because 12 cannot be equal to 5. Therefore, the original equation -4(2x - 3) = -8x + 5 has no solution.

In general, to solve equations, simplify them step by step, combining like terms and applying the rules of arithmetic and algebra. Make sure to avoid any errors or contradictions in the calculations.