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Exercise 1:

Explain what the following notations mean:

a. f : x 3x+7 : the function f that associates the number 3x+7 to any number x.

b. f(x)= -2x+3 : the function f defined by the image of any number x is -2x+3

Exercise 2:

Among the given functions, indicate which are affine, which are linear, and which are not affine.

is affine .

is affine.

is linear

is affine, it is a constant function.

is neither linear nor affine.

is linear.

is neither linear nor affine.

is neither linear nor affine.

Exercise 3:

The function f is defined by : x -5x+2.

a. Compute f(2)=-8 ;f(- 3)=17 ; f(0)=2.

b. Calculate the image of 4: f(4)= -18

c. Calculate the number x such that :

.

Exercise 4:

We give the images of two numbers by an affine function f.

f(3)=5 and f(7)=13

a. Draw its graphical representation in a reference frame.

b. Determine the algebraic expression of this function f : x ax+b (i.e. determine a and b).

so

**Conclusion:** ** **

Exercise 6:

**g(x)=3x**

**u(x)=2**

**f(x)=x+2.5**

**h(x)=-2x-2**

**k(x)=-3.5x+0.5**

Exercise 7:

The lines are parallel because the directrix is the same.

Exercise 8:

a. For rate 1, he will pay 100 €.

For rate 2, he will pay: 40+12×1=52 €.

For rate 3, he will pay: 12×2= 24 €.

In this case, rate 3 is the most interesting.

b. We call x the number of times that Yéro will go to the pool.

Express, as a function of x :

_{t1}(x)=100

_{t2}(x)= x+40

_{t3}(x)= 2x

c. Graphically represent these three functions in the same orthogonal reference frame.

d. He will have to pay 12×4 = 48 entries.

What if he goes twice a week?

double that is 96 entries.

**e. **For 48 entries, it is rate 2 and for 96 it is rate 1.

f. From 61 entries on, rate 1 is the most interesting.

Exercise 9:

1)Be the affine function f defined by f(x)=-2x+3 .

a) calculate f(0) .

f(0)= -2×0+3=3

b) calculate the antecedent of 5 .

fx()=5

-2x+3=5

-2x=5-3

-2x=2

x=-1

Therefore the antecedent of 5 by the function f is – 1 .

2) Let the affine function g be such that g(-2)=-2 and g(3)=4 .

a) determine the function g .

and

**Conclusion :** the affine function g is

b) calculate g(0) and g(3) .

3) in the same reference frame (O,I,J).

a) draw the graphical representations of f and g .

b) calculate the coordinates of the point of intersection of these graphs.

Let’s solve for f(x) = g(x)

and

The coordinates of the intersection point are: .

Exercise 10:

For the payment of the daycare in a school, two formulas are proposed.

– Formula A : you pay 40 € to become a member for the school year then you

pays 10 € per month for daycare.

Formula B: for non-members, we page 18 € per month.

1. The number of months of daycare is .

and

2. Graph the following functions in a reference frame:

and .

We will take 1 cm for 1 month in abscissa and 1 cm for 10 € in ordinate.

3.

a) This is the point of intersection of the two lines. For 9 months, the prices to be paid are equal.

b) Find this result by calculation.

4. The most advantageous if you only pay for 4 months in a year is formula B.

5. We have a budget of 113 €.

We have to solve this equation:

We will be able to pay for a maximum of 7 months of daycare with a budget of 113 euros.

Exercise 11:

In each of the following cases, write the function f as f(x)=ax+b

and specify the values of a and b.

1) The graphical representation of f is a straight line of direction -3 and such that f(0)=2.

a= – 3 so f(x)=-3x+b

and f(0)= – 2

therefore -3×0+b= – 2

b= – 2

so f ** (x)= – 3x – 2 **

2)The function f is the function that adds 6 to a number x and multiplies the result by – 4.

f(x)= – 4(x+6) = -4x-24

3) The function f is the function that, to a number x, multiplies it by 3, adds 4 to the result,

then divide it by 2.

4) The function f is defined by f(x)=(x+1)²-x².

5). The function f is such that if the x’s increase by 3, the “f(x)” increases by 12.

Moreover, f(0)=1.

and f(x)=4x+b

moreover f(0)=4×0+b=1

so b=1

where **f(x) = 4x+1**

Exercise 12:

We designate by the height SK (expressed in meters) of the SABCD pyramid.

1) Show that the volume (in^{m3}) of the greenhouse is given by the formula *
x
* .

2) Calculate this volume for *
x
* = 1,5.

3) For what value of is the volume of the greenhouse 200^{m3}?

The height of the pyramid must be 3.25 m so that the volume is 200 .

Exercise 13:

1. Complete the table.

2. a.

b.

3.

4.

a. For 6 cartridges, price A is the most advantageous.

b. For 80 euros, it is more interesting to choose formula B.

5.

Let’s find out for which number of cartridges the prices are equal:

Prices are equal for 8 cartridges purchased.

The internet price is lower for more than 8 cartridges.

Exercise 14:

The school decides to test a software to manage its library. She downloads this software on

Internet.

1. The file is 3.5 MB (Mega-bytes) in size and takes 7 seconds to download.

**What is the speed of the Internet connection? The result will be given in MB/s.**

it is a situation of proportionality.

so

After a 1 month trial period, the school decides to purchase the software.

__There are three rates:__

– Rate A: 19 €.

– Rate B: 10 cents per student

– Rate C : 8 € + 5 cents per student

2. Complete the following table:

Number of students | 100 | 200 | 300 |

Rate A | 19 € | ||

Rate B | 30 € | ||

Rate C | 18 € |

3. a. If x represents the number of students, which of the following expressions corresponds to rate C?

C1 = 8 + 5x

**C2 = 8 + 0.05x**

C3 = 0.05 + 8x

b. Is this a situation of proportionality? Justify the answer.

C2 corresponds to an affine function, so it is not a situation of proportionality, there should have been a linear function (it is the case of tariff B).

Exercise 17:

a. The total area is :

.

b. x is between 0 and 5.

c.

d.

e. We observe graphically that the wishes of the librarian

will be taken into account when x = 5.

and by calculation :

10x=65-5x

10x+5x=65

15x=65

## The answers to the math exercises on affine functions in 3rd grade.

After having consulted **the answers to these exercises on affine functions** in 3rd grade, you can return to the **exercises in 3rd grade****.**

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