Question

Could someone answer and explain these to me? That would be great, thanks!

Answer 1

These are two questions and two answers.

Question 1. When y = x², which of the following expressions is equivalent to - y?

Answer: the option G. -x².

Step-by-step explanation:

The important thing is to be careful with the use of the negative sign before the function because a typical mistake is to incorporate the negative sign inside the parentheses, which yields to square it resulting, mistakenly, in a positive value.

The correct steps are:

• Given y = x², find - y

• Muliply both sides of the equation by - 1: - y = - (x²)

• Delete the negative sign before the parentheses: - y = - x².

So, the answer is the option G.

Question 2. For the function h(x) = 4x² - 5x, what is the value of h(-3)?

Answer: option D. 51

Step-by-step explanation:

Since, you have the explicit function h(x), to find h(-3), you just must subsititute the variable x with -3.

This is how you do it:

• Given: h(x) = 4x² - 5x

• Find h(-3) ⇒ substitute x = - 3

• h(-3) = 4(-3)² - 5(-3) = 4(9) + 15 = 36 + 15 = 51 ← answer (option D.)

Answer 2

y=-x^2

Step-by-step explanation:

given that y = x^2 is the function.

For equivalent to -y, we can multiply this equation both the sides by -1

We get -y = -x^2

Hence option G is right.

Also y =x^2 is a parabola with vertex at origin open up.

Hence if F is selected we get -y =(-x)^2 = x^2, this will make the parabola open down and hence this option is wrong.

H: -y=-x is wrong because this represents a line but we had original equation as that of a parabola

J) -y = x^(-2) means x^2y =-1

This implies that rate of change of y = 2/x^3 but rate of change of y has to equal 2x since y = x^2 is original. Hence only option G is right.