HELP! Giving out free points if you answer right!! What is the average rate of change from x=0 to x=1

(Graph in photo)

Explanation:

Mark the points (0,-3) and (1,0) which are on the blue parabola. These points have x coordinates x = 0 and x = 1. This corresponds to the interval your teacher provided.

Finding the slope of the line through the two points mentioned will find the average rate of change.

m = slope

m = (y2-y1)/(x2-x1)

m = (0-(-3))/(1-0)

m = (0+3)/(1-0)

m = 3/1

m = 3

If you started at (0,-3), moved up three units and then to the right one unit, you'd arrive at (1,0). This visually confirms we have the right slope.

Since the slope is 3, the average rate of change is 3.

As an alternative, you could use the average rate of change (AROC) formula

AROC = ( f(x2) - f(x1) )/(x2 - x1)

But note how f(x2) and f(x1) are y2 and y1, but in a different format. So we're just using the slope formula here. Both methods are effectively the same.

3

Step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

hi im bob : l

step-by-step explanation: