Asap ! ! 3. consider the functions f(x) = x2 + 10x – 5, g(x) = 8x + 1, and h(x) = 3x – 4. list the functions from least to greatest value when x = 3 and when x = 6. then tell how you would explain to someone that you do not need to do any calculations to know the order of the functions when x = 15.

The order from least to greatest is: h(x), g(x), f(x)

This is true for x = 3, x = 6, and x = 15

The function values are given in a table as shown in the attached image.

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Explanation:

For each function, we replace x with the specified value. Then we compare the outputs to see which is larger.

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Let's plug x = 3 into each function

Start with f(x)

f(x) = x^2 + 10x - 5

f(3) = (3)^2 + 10(3) - 5

f(3) = 34 ... use a calculator, or PEMDAS

Repeat for g(x)

g(x) = 8x+1

g(3) = 8(3)+1

g(3) = 25

and then h(x)

h(x) = 3x-4

h(3) = 3(3)-4

h(3) = 5

The order from least to greatest is h(x), g(x), f(x)

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Let's plug x = 6 into each function

Start with f(x)

f(x) = x^2 + 10x - 5

f(6) = (6)^2 + 10(6) - 5

f(6) = 91

Repeat for g(x)

g(x) = 8x+1

g(6) = 8(6)+1

g(6) = 49

and then h(x)

h(x) = 3x-4

h(6) = 3(6)-4

h(6) = 14

The order from least to greatest is h(x), g(x), f(x)

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You don't need to plug x = 15 into each function to know that h is the smallest, followed by g, then f being the largest. This is because the linear functions always have the slowest growth compared to quadratic functions. So f(x) being quadratic is the largest output of all three. The smaller of the linear outputs happens with the smaller slope. Recall that slope is rate of change telling us how fast a function grows (assuming the slope is positive). We see that h(x) has slope 3 compared to g(x) that has a slope of 8

Check out the attached image below. Note how everything to the right of point C, with x coordinate 1.65, is where the functions do not cross one another anymore. Beyond this point, h(x) is always the smallest with slowest growth, followed by g(x) in the middle, and then f(x) is the fastest growing function with the largest outputs for any one single input.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

college