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.

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!