All categories

2 years ago

PLEASE HELPselect the algebraic definition for the piece wise function graph

Mathematics

1 answer:

Sedaia [141]2 years ago

8 0

Answers:

4 goes in the first box

-2x+8 goes in the second box

===========================================================

Explanation:

This piecewise function has 3 separate components to it:

The left-most piece is the line labeled with 2x+4. This is why it's listed first in the algebraic definition (i.e. your teacher already filled this part out for you). This piece applies only when -2 <= x < 0
The center piece is y = 4. We leave the "y = " portion out and simply write 4 as the center piece. This says that the output is 4, but only when 0 <= x < 2. That will graph out a flat horizontal portion as the graph shows.
Lastly, the right-most piece is the line y = -2x+8. Again, we leave off the y portion and just write -2x+8. This piece only applies when 2 <= x < 4

Side note: Something like 2 <= x is another way of saying $2 \le x$

You might be interested in

Find the average rate of change of k(x)=5x–19 over the interval [ - 14, - 4].

rusak2 [61]

The rate of change of a function can be modeled with the following expression:

$\frac{\Delta{k{x)}}{\Delta{x}}$

Where Δx is the change in x value, and Δk(x) is the corresponding change in k(x). We're given the two extremes of x, so we can calculate the change in x to be

$\Delta{x}=-4-(-14)=10$

To find the change in k(x), we can calculate the values of k(x) at x = -14 and x = -4 and find the difference between them:

$k(-14)=5(-14)-19=-70-19=-89\\ k(-4)=5(-4)-19=-20-19=-39\\ \Delta{y}=k(-14)-k(-4)=-89-(-39)=-50$

So, the rate of change for the function from x = -14 to x = -4 is

$\frac{\Delta{y}}{\Delta{x}}= \frac{-50}{10}=-5$

7 0

3 years ago

Marques drops a plate from a height of 5 feet. When will the plate hit the ground?

nadya68 [22]

Answer:

Option A. about 1 seconds

Step-by-step explanation:

Let the initial speed u and the final speed v

Time t , distance s and acceleration of gravity g

The equation of motion are:

v = u + gt ⇒(1)

s = ut + 0.5 gt² ⇒(2)

v² = u² + 2gs ⇒(3)

Marques drops a plate from a height of 5 feet.

So, u = 0 , s = 5 ft , g = 9.8 m/sec²

Substitute at (2)

s = ut + 0.5 gt²

5 = 0 * t + 0.5 * 10 * t²

∴ t² = 5/(0.5*9.8) = 1.02

∴ t = √1.02 = 1.01 seconds ≈ 1 seconds (to the nearest integer)

The answer is option A. about 1 seconds

4 0

3 years ago

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 –

SVETLANKA909090 [29]

We have to identify the function which has the same set of potential rational roots as the function $g(x)= 3x^5-2x^4+9x^3-x^2+12$ .

Firstly, we will find the rational roots of the given function.

Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Consider the first function given in part A.

f(x) = $3x^5-2x^4-9x^3+x^2-12$

Here also, Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Therefore, this equation has same rational roots of the given function.

Option A is the correct answer.

4 0

2 years ago

Read 2 more answers

Which statement is true about the solutions for the equation 5y + 8 = −2?

amm1812

5y=-10

Y=-2 it has one solution

3 0

2 years ago

Read 2 more answers

Please Help Please help. See the picture

Gwar [14]

Answer:

• General equation of a line is as below:

${ \boxed{ \tt{y = mx + c}}} \\$

→ m is the slope

${ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\$

• Consider points (0, 3) and (3, 0) from the graph:

${ \tt{slope = \frac{0 - 3}{3 - 0} = \frac{ - 3}{3} }} \\ \\ { \tt{ \underline{ \: \: slope = - 1 \: \: }}}$

→ c is the y-intercept:

• consider point (0, 3):

${ \tt{y = mx + c}} \\ { \tt{3 = ( - 1 \times 0) + c}} \\ { \tt{c = 3}}$

» Therefore, substitute to make the equation of a line:

${ \boxed{ \boxed{ \tt{ \: \: y = - x + 3 \: \: }}}}$

7 0

2 years ago