Verify if the points belong to the graph of f(x)=5-x?

A(2,3) B(-1,4)

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To verify if A(2,3) and B(-1,4) belongs to f(x) = 5-x.

Solution:

We substitute the coordinates of x and of A and B in y = f(x) = 5-x and see if they satisfy:

A(2,3): y = 5-x . LHS = 3. RHS = 5-2 =3. SoA satisfies.

B(-1,4): y= 5-x. LHS = 4. RHS = 5--1 = 5+1. B does not satisfy.

For a point to belong to a graph, it's coordinates have to verify the expressio of the function.

We'll verify if the point A is on the graph, substituting it's coordonates into the expression of the function.

f(x)=5-x, where f(x)=y

So, yA = 5-xA

3 = 5-2

3=3

The point A(2,3) is on the graph pf the function f.

We'll check if the point B(-1,4) is on the graph.

yB = 5-xB

4 = 5-(-1)

4 = 5+1

4 = 6

The point B(-1,4) is not on the graph of f.

f(x) = 5-x

To verify of the points belong to the graph of f(x), then the points should verify the equation:

For point A (2,3) , we need to verify if f(2)=3

f(2) = 5-2 = 3

The A belongs to the graph of f(x)

For Point B(-1,4), we need to verify if f(-1)=4

f(-1) = 5-(-1) = 5+1 =6

Then the point B DOES not belong to the graph of f(x).

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