# Linear functions: math exercises in 3rd grade corrected in PDF.

Linear functions in third grade math are necessary for student progress. This will allow you to develop skills. Also, linear functions in math are to be learned entirely.

The notion of proportionality between two quantities necessarily intervenes.

You will find in these exercises all the notions concerning the linary functions (image, antecedent, drawing of the curve).

 Tomato sales. Price per kilo : 2 € .

Proportionality:

1. Show that the price paid y (in €) is proportional to the mass of tomatoes x (in kg) purchased.

2. Establish the relationship between y and x .

3. The coefficient of proportionality is a = ….. .

These two quantities are proportional, so the price paid is a linear function of the mass of tomatoes purchased.

Study of the linear function :

Let the linear function, denoted by

f : x f(x)

(mass of tomatoes ® price paid)

1. What is the relationship between f(x) and x?

f(x) = ………

1. Justify the fact that f is a linear function.
1. Calculate f(3) ; f(0) ; f( 5) .
1. Calculate the image of 7 by the function f .
2. What is the concrete meaning of the result?
3. What is the number with image 5?

(f : ? 5 )

7. What is the number whose image is 6.5?

(f : ? 6,5 )

8. Complete the following table using the previous results:

 x 0 3 5 7 f(x) 5 6,5 Points O A B C

9. In an orthogonal reference frame, represent the curve of the function f .

Graphic units :

• – Abscissa: 1 cm 1 kg.
• – Ordinates: 1 cm 2 € .

9. Determine graphically:

(leave the construction lines visible)

– The price of 3.5 kg of tomatoes ;

– The mass of tomatoes bought for 8 euros .

See the correction

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