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sweet [91]
3 years ago
14

For the linear function f(x) = -2x+1 , find the following

Mathematics
1 answer:
Leya [2.2K]3 years ago
4 0

Given:

The function is:

f(x)=-2x+1

To find:

a. Slope and Y-intercept.

b. Is the function increasing, decreasing, or constant, justify your answer.

c. Graph the function, label x, and y-intercepts.

Solution:

a. We have,

f(x)=-2x+1                  ...(i)

The slope intercept form of a line is:

y=mx+b                    ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

m=-2,b=1

Therefore, the slope of the line is -2 and the y-intercept is 1.

b. If the slope of a linear function is negative, then the function is decreasing.

If the slope of a linear function is positive, then the function is increasing.

If the slope of a linear function is 0, then the function is constant.

The slope of the linear function is negative.

Therefore, the function is decreasing.

c. We have,

f(x)=-2x+1

At x=0, we get

f(0)=-2(0)+1

f(0)=1

So, the y-intercept is at (0,1).

At f(x)=0, we get

0=-2x+1

2x=1

x=\dfrac{1}{2}

x=0.5

So, the x-intercept is at \left(0.5,0\right).

Plot the points (0,1), \left(0.5,0\right) and connect them by a straight line as shown below:

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Rewrite the equation below in standard form.
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3 0
3 years ago
Find the radius and diameter of circle A, if the endpoints of the radius<br> are (-2, -1) and (6,4).
AleksandrR [38]

Step-by-step explanation:

length \: between \: ( - 2, - 1) \: and \: (6,4) \\  =  \sqrt{(x _{1} - x  _{2} )² + (y _{1}  - y _{2})²  }  \\  =  \sqrt{( -  2 - 6)²+ ( - 1 - 4)²}  \\  =   \sqrt{64 + 25}  \\  =  \sqrt{100}  \\  = 10 \: units \\ radius = 10 \: units \\ diameter = 2 \times radius \\ d = 2 \times 10 \\ d = 20 \: units

8 0
3 years ago
What is 9/10 divided by 3/4?
goldenfox [79]

Answer:

6/5

Step-by-step explanation:

hi! when dividing fractions, we use the KCF rule, which stands for keep,change,flip. we keep the first fraction the same, change the division symbol to multiplication, and flip the second fraction to its reciprocal. therefore, we now have:

9/10 * 4/3

now, we can multiply the numerators and denominators.

36/30

we can simplify this.

6/5

7 0
3 years ago
Read 2 more answers
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ASHA 777 [7]

Answer:

1. Growth 2. it growth but then just plug in the number of tdays for the rest of them

Step-by-step explanation:

3 0
3 years ago
3. Which relation is a function?
Pani-rosa [81]

Answer:

B

Step-by-step explanation:

Recall that functions are defined only if for each value in the domain produces one and only one value in the range.

If we view the relations in the questions as x-y coordinates, this means that for every x-value, you can only have one y-value

Lets evaluate the options:

A) we can see that for x = -3, this gives 2 possible values for y i.e (-3,4) and (-3,8) (hence this is not a function)

C) we can see that for x = 3, this gives 2 possible values for y i.e (3,-8) and (3,8) (hence this is not a function)

D) we can see that for x = -3, this gives 2 possible values for y i.e (-3,4) and (-3,8) (hence this is not a function)

the only choice where this doesn't occur is choice B

6 0
3 years ago
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