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aleksandrvk [35]
3 years ago
8

The function f(x) = - (x + 5) * (x + 1) shown What is the range of the function ? 10 all real numbers loss than or equal to all

roal numbers less than or equal to -3 all real numbers groater or equal to 4 numbors greater than or equal to -6
Mathematics
1 answer:
pshichka [43]3 years ago
6 0

Given:

The function is:

f(x)=-(x+5)(x+1)

To find:

The range of the function.

Solution:

We have,

f(x)=-(x+5)(x+1)

It can be written as:

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

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

Add and subtract square of half of coefficient of x, i.e., \left(\dfrac{6}{2}\right)^2=9.

f(x)=-(x^2+6x+9-9+5)

f(x)=-(x^2+2(x)(3)+3^2-4)

f(x)=-(x^2+2(x)(3)+3^2)+4

f(x)=-(x+3)^2+4

On comparing this equation with f(x)=a(x-h)^2+k, we get

a=-1, it means the graph of the function is a downward parabola and the vertex is the point of maxima.

h=-3

k=4

The vertex of the function is (-3,4). So, the value of the function cannot be greater than 4.

Therefore, the range of the function is all real numbers less than or equal to 4.

Note: All options are incorrect.

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Answer:

Part 2

The rate of change is 1 in increase in forearm length per 1 inch increase in foot length

Part 3

1) Foot length = 17.922 in.

2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860

3) No the data does not correspond with part A

4) The data  presented here has a greater rate of change

5) Different data sources

6) Yes

7) Yes

Step-by-step explanation:

Part 2

The data are as follows

Forearm             Foot

9.25                    8.5

10.25                   9.5

9.75                     9

10.75                    10

8.75                       8

To find the rate of change, we have;

For points

(x₁, y₁) = (9.25, 8.5) and (x₂, y₂) = (8.75, 8) we have;

Rate of change = (y₂ - y₁)/(x₂ - x₁) substituting the values we arrive at

(8.75 - 9.25)/(8 - 8.5) = 1

The rate of increase of foot to forearm is 1 to 1. That is there is an increase of 1 in in forearm length for every inch increase in foot length

The rate of change is 1 in increase in forearm length per 1 inch increse in foot length

Part 3

1) For a person with length of forearm, x = 17 inches long, we have;

Length of foot, y = 0.860·x + 3.302

Plugging in the values, we have;

y = 0.860×17 + 3.302 = 17.922 in.

2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860

3) No the data does not correspond with part A

4) The rate of change from part A = 0.860, Therefore, the data  presented here has a greater rate of change

5) The values are different because of they are derived from a non corresponding sources

6) Yes the relation is a function because the length of the foot is a function of the length of the forearm

From the equation of a straight line, we have;

y = mx + c

Where:

m = Slope = 1

Therefore; for forearm, y = 9.25, we have

9.25 = 1×8.5 + c

∴ c = 9.5 - 8.5 = 1

The equation of the function becomes;

y = x + 1

7) for the equation in part A given by

y = 0.860·x + 3.302

Yes the equation in part A can represent a function because it maps each value of x to a unique value of y

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