All categories

3 years ago

Consider the table of values for functions f and g below.

Mathematics

1 answer:

AlexFokin [52]3 years ago

6 0

Answer:

A. For every value of x, the rate of change of f exceeds the rate of change of g.

FALSE

Because the rate of change of f increases from 4 to 294, while the rate of change of g is constant (8).

B. As x increases, the rate of change of g exceeds the rate of change of f.

FALSE.

Because the rate of change of g is 8 (constant) and the rate of change of f starts at 4 and increases exceeding that of g.

C. At x = 2, the rate of change of f is equal to the rate of change of g.

FALSE

At x = 2 the rate of change of f is 12 and the rate of change of g is 8.

D. As x increases, the rate of change of f exceeds the rate of change of g.

TRUE

The rate of change of f at start is 4 and increases to 294, while the rate of change of g is 8 (constant), so as x increases, the rate of change of f exceeds the rate of change of g.

Explanation:

The rate of change of a function is calculated as:

rate of change = rise / run = change in y / change in x = Δy / Δx

For f(x) you get the following rates of change:

x f(x) Δy Δx Δy/Δx

0 3 - - -

1 7 7-3 = 4 1 - 0 = 1 4/1 = 4

2 19 19 - 7 = 12 2 - 1 = 1 12/1 = 12

3 55 55 - 19 = 36 3 - 2 = 1 36

4 163 163 - 55 = 108 4 - 3 = 2 108

5 457 457 - 163 = 294 5 - 4 = 1 294

From that, you see that the function f(x) is an increasing function with an increasing rate of change in the interval [0,5].

For g(x) you get f(x) you get the following rates of change:

x g(x) Δy Δx Δy/Δx

0 3

1 11 11 - 3 = 8 1 - 0 = 1 8

2 19 19 - 11 = 8 2 - 1 = 1 8

3 27 27 - 19 = 8 3 - 2 = 1 8

4 35 35 - 27 = 8 4 - 3 = 1 8

5 43 43 - 35 = 8 5 - 4 = 1 8

From that you can see that the function f(x) is increasing linear function, so its rates of change is constant.

You might be interested in

If point E exists such that its x-coordinate is 12 and ED is parallel to AC, then what is the y-coordinate of point E? Show how

makkiz [27]

I have to see if you can get it done before the first day of the shower

8 0

3 years ago

What is the answer for <br> 7(-9)

Cerrena [4.2K]

Answer:

-63

Step-by-step explanation:

7×9= 63

7 × -9 = -63

Hope this helps!

5 0

3 years ago

Please help me with this math problem (simplify the expressions and please show work)

JulijaS [17]

9514 1404 393

Answer:

10x^6

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)(a^c) = a^(b+c)

$(5x^4y^5)(2x^2y^{-5})=(5)(2)(x^{4+2})(y^{5-5})=10x^6y^0=\boxed{10x^6}$

8 0

3 years ago

LINEAR ALGEBRA

kenny6666 [7]

Answer:

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

Step-by-step explanation:

Let be $\vec u_{1} = [2,3,1]$ , $\vec u_{2} = [4,1,0]$ and $\vec u_{3} = [1, 2,k]$ , $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{3}$ if and only if:

$\alpha_{1} \cdot \vec u_{1} + \alpha_{2} \cdot \vec u_{2} +\alpha_{3}\cdot \vec u_{3} = \vec O$ (Eq. 1)

Where:

$\alpha_{1}$ , $\alpha_{2}$ , $\alpha_{3}$ - Scalar coefficients of linear combination, dimensionless.

By dividing each term by $\alpha_{3}$ :

$\lambda_{1}\cdot \vec u_{1} + \lambda_{2}\cdot \vec u_{3} = -\vec u_{3}$

$\vec u_{3}=-\lambda_{1}\cdot \vec u_{1}-\lambda_{2}\cdot \vec u_{2}$ (Eq. 2)

$\vec O$ - Zero vector, dimensionless.

And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:

$[1,2,k] = -\lambda_{1}\cdot [2,3,1]-\lambda_{2}\cdot [4,1,0]$