Test Functii

1. Se considera functia liniara a carei expresii este f(x) = 2x +5. Stabiliti valoarea de adevar pentru afirmatia : "Punctul A( 2: 9)

"

Fals

Adevarat

The statement "Punctul A(2, 9)" is true because when we substitute x=2 into the linear function f(x) = 2x + 5, we get f(2) = 2(2) + 5 = 4 + 5 = 9. Therefore, the coordinates of point A (2, 9) satisfy the given linear function.

Explanation

The statement "Punctul A(2, 9)" is true because when we substitute x=2 into the linear function f(x) = 2x + 5, we get f(2) = 2(2) + 5 = 4 + 5 = 9. Therefore, the coordinates of point A (2, 9) satisfy the given linear function.

2. Se considera functia liniara a carei expresii este f(x) = 2x - 7. Stabiliti valoarea de adevar pentru afirmatia : "Punctul A( 2: -5)

"

Adevarat

Fals

The given function is f(x) = 2x - 7. To determine the truth value of the statement "Point A(2, -5)", we need to substitute the x-coordinate (2) into the function and check if the result matches the y-coordinate (-5) of the point.

When we substitute x = 2 into the function, we get f(2) = 2(2) - 7 = -3. Since -3 does not match the y-coordinate (-5) of point A, the statement "Point A(2, -5)" is false.

Explanation

The given function is f(x) = 2x - 7. To determine the truth value of the statement "Point A(2, -5)", we need to substitute the x-coordinate (2) into the function and check if the result matches the y-coordinate (-5) of the point.

When we substitute x = 2 into the function, we get f(2) = 2(2) - 7 = -3. Since -3 does not match the y-coordinate (-5) of point A, the statement "Point A(2, -5)" is false.

3. Se considera functia

Punctul de pe grafic care are coordonatele egale este :

( 2 ; 3)

( 3 : 3 )

(5; 5)

(3; 2)

The point on the graph that has equal coordinates is (5, 5). This means that both the x-coordinate and the y-coordinate of this point are the same, which is 5. Therefore, (5, 5) is the correct answer.

Explanation

The point on the graph that has equal coordinates is (5, 5). This means that both the x-coordinate and the y-coordinate of this point are the same, which is 5. Therefore, (5, 5) is the correct answer.

4. Daca

este un punct pe graficul functiei

8

6

4

2

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Explanation

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5. Alegeti varianta corecta. Daca

A =1 si b = 2

A = 2 si b = 1

A = 1 si b = 3

A = 3 si b = 1

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Explanation

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6. Pentru functia liniara f descrisa de relatia f(x) = 3x - 6 , punctul de intersectie a graficului cu abscisa (axa ox) are coordonatele :

(0, -6)

(-6, 0)

(0, 2)

(2, 0)

The given linear function is f(x) = 3x - 6. To find the point of intersection with the x-axis, we set f(x) = 0 and solve for x.

0 = 3x - 6

Adding 6 to both sides, we get:

6 = 3x

Dividing both sides by 3, we find:

2 = x

Therefore, the point of intersection with the x-axis has coordinates (2, 0).

Explanation

The given linear function is f(x) = 3x - 6. To find the point of intersection with the x-axis, we set f(x) = 0 and solve for x.

0 = 3x - 6

Adding 6 to both sides, we get:

6 = 3x

Dividing both sides by 3, we find:

2 = x

Therefore, the point of intersection with the x-axis has coordinates (2, 0).

7. Daca graficul unei functii liniare este dreapta AB unde A(0:4) iar B(3:0) atunci distanta de la punctul de intersectie a axelor O la dreapta AB este .... u.

3,4

2,4

5

7

The correct answer is 2,4. In this question, we are given that the graph of a linear function is a straight line AB, where A(0,4) and B(3,0). The distance from the point of intersection of the axes O to the line AB can be found by calculating the length of the perpendicular segment from O to AB. By drawing a perpendicular from O to AB, we can see that it intersects AB at the point C(2,4). Therefore, the distance from O to AB is the length of the segment OC, which is 2 units on the x-axis and 4 units on the y-axis, giving us the answer 2,4.

Explanation

The correct answer is 2,4. In this question, we are given that the graph of a linear function is a straight line AB, where A(0,4) and B(3,0). The distance from the point of intersection of the axes O to the line AB can be found by calculating the length of the perpendicular segment from O to AB. By drawing a perpendicular from O to AB, we can see that it intersects AB at the point C(2,4). Therefore, the distance from O to AB is the length of the segment OC, which is 2 units on the x-axis and 4 units on the y-axis, giving us the answer 2,4.

8. Fie f si g doua functii liniare , daca f(x) = 2x + 1 si g(x) = -x +1 reprezentate in acelasi sistem de axe , atunci punctul de intersectie a celor doua grafice are coordonatele ...

( 0,1)

(1,0)

(1,1)

(0,0)

The intersection point of two linear functions can be found by setting the two functions equal to each other and solving for the variable. In this case, setting f(x) equal to g(x) gives 2x + 1 = -x + 1. Simplifying this equation gives 3x = 0, which implies that x = 0. Plugging this value back into either of the original functions gives y = 1. Therefore, the coordinates of the intersection point are (0, 1).

Explanation

The intersection point of two linear functions can be found by setting the two functions equal to each other and solving for the variable. In this case, setting f(x) equal to g(x) gives 2x + 1 = -x + 1. Simplifying this equation gives 3x = 0, which implies that x = 0. Plugging this value back into either of the original functions gives y = 1. Therefore, the coordinates of the intersection point are (0, 1).

9. Punctele A(2, 3) , B( 3, 5) si C(4; 7) sunt coliniare?

DA

NU

The points A(2, 3), B(3, 5), and C(4, 7) are not collinear because they do not lie on the same straight line. Collinear points are points that lie on the same line, but in this case, the three points do not form a straight line. Therefore, the correct answer is "NU" (NO).

Explanation

The points A(2, 3), B(3, 5), and C(4, 7) are not collinear because they do not lie on the same straight line. Collinear points are points that lie on the same line, but in this case, the three points do not form a straight line. Therefore, the correct answer is "NU" (NO).