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The answer key to the math exercises in 3ème on linear functions.

Calculate images and priors. To work on the curve of a linear function and to exploit a table of values.

Exercise 1:

Let be the linear function f : x 1,2x.

a. Calculate f(5); f(- 1,2); f(0); f(100).

f(5)=1,2×5=6 ; f(-1,2)=- 1,44 ; f(0)= 0 ; f(100 ) = 120

b. Compute the numbers x whose images are 2400 ; – 45.

Exercise 2:

Let g be the linear function such that g 😡 – 0.4x.

a. What is the coefficient of the function g?

a = – 0,4

b. Calculate the images of 10; – 5 and 1.

g(10) = – 4; g(-5)=2; g(1) = -0.4

Exercise 3:

We know that 18 has the image of 23 by the function f and that 12 has the image of 14 by f.

Is f a linear function? why?

Let’s compare and :

The fractions are not equal so it is not a linear function.

Exercise 4:

Express the linear function f in the form ( the number a is to be determined), then calculate f(0); f(1) and f( – 2).

1. When the image of 10 is – 3.

We have so f is such that .

2. When f (- 100)= – 46.

We have so f is such that .

3. When the coefficient of f is 2.5.

We have f which is defined by .

Exercise 5:

In a reference frame, it is enough to know the coordinates of a single point ( **whose abscissa is non-zero**) belonging to the curve of a linear function to draw it.

a. For .

We have f(2)=2.5×2 = 5 so the curve passes through the point A(2;5).

b. Draw the line d of equation y = 1.2x, we will note this function h.

We have h(5)=1,2×5=6 so the curve passes through the point B ( 5 ; 6).

c. Draw the line d’ representing the linear function g of coefficient a = – 2.

We have g(1)= – 2 so the curve passes through C(1;- 2).

Here are the curves of these three linear functions:

Exercise 10:

Here are the curves of these five linear functions.

y=2.5x is (d1)

y= – 3x is (d5)

ets (d3)

is (d2)

is (d4)

Exercise 14:

f is a linear function. Determine the expression of f(x)

f is of type .

Conclusion:

Exercise 15:

a) Let: x be the initial price of an item and: y its final price after an increase or decrease. What is the percentage increase or decrease in each of the following cases? (1): y = 1.4x

** That’s a 40% increase. **

(2): y = 0.5x

**That’s a 50% reduction.**

(3): y = 0.9x

**That’s a 10% reduction.**

(4): y = 1.05x

** That’s a 5% increase. **

Exercise 16:

1. An object A costs 65 euros. Its price increases by 5%.

How much does it cost after this increase?

The multiplying factor is .

** The final price is 68.25 euros. **

2. object B costs 88 euros after a 10% increase.

What was its price before this increase?

The multiplying factor is .

** The price before increase is 80 euros. **

3. an object C costs 45 euros. After an increase its price is 50,40 euros.

What is the percentage of this increase?

The multiplying factor is

** The increase was 12%. **

Exercise 17:

A clothing store manager decides to lower his prices by 15%.

a) What is the linear function modeling this decrease?

**The linear function modeling a 15% decline is f(x)=0.85x .**

b) What is the new price of a pair of pants that cost 70 e before this decrease?

**f(70)=0.85×70=59.5 €.**

c) What is the old price of a sweater that costs 50,12 € after this decrease?

We look for x such that f(x)=50.12

where 0.85x=50.12

or

**Conclusion: ** **the old price of the sweater was 56 € .**

Exercise 18:

Consider the linear function f with coefficient – 5.

So we have **f(x)= – 5x**

Calculate the image by f of the following numbers:

a) 0

f(0)=0 (f is a linear function).

b) 3

c) – 2

d)

e)

Exercise 19:

For each function, specify whether it is linear and, if so, its coefficient.

a)

It is linear with coefficient a= 3,5 .

b)

it is not linear, it is an affine function.

c)

it is not linear, it is a square function.

d)

it is linear with coefficient a= – 1 .

e)

it is not linear, it is a constant function.

f)

it is linear with coefficient .

Exercise 20:

a.

b.

c.

A product of factors is zero if and only if at least one of the factors is zero.

** Conclusion : The numbers 0 and 4 have the same image by V1 and V2 .**

Exercise 21:

Let f be the linear function defined by: .

1. Calculate f(3), f( – 2), f(7).

2. What are the images by f of – 1, 6, ?

3. Find the number whose image is 7.

## The answer key to the math exercises on linear functions in 3rd grade.

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

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