Question

Which of the following functions functions has a rate of change that stays the same?

Answer 1

Answer:

y = 2x   and y = -7x +9

Step-by-step explanation:

The two "linear" functions are those that have a constant rate of change. Actually, the slope (inclination) they show when plotted is that "rate of change".

The function : y = 2x, has a constant positive rate given by its slope (2).

The function : y= -7x +9 has a constant negative rate given by its slope (-7)

The other two functions are quadratic, represented by parabolas, and therefore don't have a constant rate of change.

Answer 2

Answer:

Option B and C

Step-by-step explanation:

We are given that

1.$y=\frac{1}{3}x^2$

Differentiate w.r.t x

$\frac{dy}{dx}=\frac{2}{3}x$

By using the formula

$\frac{dx^n}{dx}=nx^{n-1}$

Rate of change of function  depend on x. Hence, it is not constant.

2.$y=2x$

$\frac{dy}{dx}=2$

The rate of change of the function does not vary wit x.

Hence, it stays the same.

3.$y=-7x+9$

$\frac{dy}{dx}=-7$

The rate of change of the function does not vary wit x.

Hence, it stays the same.

4.$y=x^2+1$

$\frac{dy}{dx}=2x$

Rate of change of function  depend on x. Hence, it is not constant.