FIND THE DOMAIN AND RANGE OF f(x)=-2x+5

Question

the question is on the topic functions and the answer can be provided using interval notation or an inequality

Answer 1

Given function f(x) = -2x+5

y = f(x)

For x = 0

y = 5

For x = 1

y = 3

For x =  -1

y = 7

Substtute x = 0,1,-1 respectively, the value of y would be 5,3,7.

x values are domain of the function.

In this case we can substitute any real number for x, we will get value of f(x).

Domain of the function is all real numbers.

Interval notation is (-∞,∞)

 

Answer 2

The equation is y = f (x ) = - 2x + 5.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x	y = - 2x + 5	(x, y)
-2	y = - 2(- 2) + 5 = 4 + 5 = 9	(- 2, 9)
- 1	y = - 2(- 1) + 5 = 2 + 5 = 7	(- 1, 7)
0	y = - 2(0) + 5 = 0 + 5 = 5	(0, 5)
1	y = - 2(1) + 5 = - 2 + 5 = 3	(1, 3)
2	y = - 2(2) + 5 = - 4 + 5 = 1	(2, 1)

Draw a coordinate plane.

Plot the coordinate points.

Then sketch the graph, connecting the points with a line.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown.

Notice that every real number is the x - coordinate of some point on the line.

Also, every real number is the y - coordinate of some point on the line.

So, the domain and range are both all real numbers, and the relation is continuous.

The range and the domain is (-∞,∞).