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3 years ago

If f(x)=4x-16andtheDomainis{-2,-1,0,3,6},findtheRange of the function. Show all work.

Mathematics

1 answer:

Svet_ta [14]3 years ago

6 0

Answer:

R={-24,-20, -16, -4, 8}

Step-by-step explanation:

f(x)=4x-16

f(-2)=4(-2)-16

f(-2)=-8-16

f(-2)=-24

f(x)=4x-16

f(-1)=4(-1)-16

f(-1)=-4-16

f(-1)=-20

f(x)=4x-16

f(0)=4(0)-16

f(0)=0-16

f(0)=-16

f(x)=4x-16

f(3)=4(3)-16

f(3)=12-16

f(3)=-4

f(x)=4x-16

f(6)=4(6)-16

f(6)=24-16

f(6)=8

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Answer:

$\frac{1}{5}$ fraction of gallon is in each bottle.

Step-by-step explanation:

As per the given condition: G.O is going on a hike in the mountains on a hot summer day he has 4/5 gallon of water that he split into 4 bottles.

⇒ in 4 bottle he has $\frac{4}{5}$ gallon of water.

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By unit rate definition,

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3 years ago

For each function, do the following: a) state the name of the function, b) identify the independent and dependent variable, c) i

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Answer:

Given the function in the question

f(x) = |x-3| + 2

a) state the name of the function

Absolute value function

since it is similar to f(x) = |x|

b) identify the independent and dependent variable

x = independent variable (input variable)

f(x) or y = dependent variable (output variable)

The variable which we assign the value we call the independent variable, and the other variable is the dependent variable, since it value depends on the independent variable.

c) identify the rule

A function is an equation that has only one answer for y for every x.

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3 years ago

You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.

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This problem seems to be wrong because no minimum point was found and no point of landing exists

Answer:

1) There is no maximum height

2) The ball will never land

Step-by-step explanation:

Derivatives

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

If f''(a) is negative, then x=a is a maximum

The function provided in the question is

$h(x)=2x^2-12x+20$

Let's find the first derivative

$h'(x)=4x-12$

solving h'=0:

$4x-12=0$

x=3

Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

To find when will the ball land, we set h=0

$2x^2-12x+20=0$