find the implied domain of the following f(x)= 9/5 x+2

Question

domain and range.

Answer 1

f(x) = (9/5)x+2

y = (9/5)x+2

If x = 0 ⇒ y = 2

If  x = 1 ⇒ y = 19/2 = 9.5

If x = -1 ⇒ y = 1/5 = 0.2

If x = 0,1,-1.. substitute in given equation then set of coordinate pair would be

y = 2,9.5,0.2...

We know that domain of function is x values.

Range of the function is y values.

Domain set is {0,1,-1} and range set is {2,9.5,0.2}.

Answer 2

The equation is y = f (x ) = (9/5)x + 2.

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 = (9/5)x + 2	(x, y )
-2	y = (9/5)(- 2) + 2 = (- 18/5) + 2 = (- 18 + 10)/5 = - 8/5.	(- 2, - 8/5)
- 1	y = (9/5)(- 1) + 2 = (- 9/5) + 2 = (- 9 + 10)/5 = 1/5.	(- 1, 1/5)
0	y = (9/5)(0) + 2 = (0) + 2 = 2.	(0, 2)
1	y = (9/5)(1) + 2 = (9/5) + 2 = (9 + 10)/5 = 19/5.	(1, 19/5)
2	y = (9/5)(2) + 2 = (18/5) + 2 = (18 + 10)/5 = 28/5.	(2, 28/5)

• Draw a coordinate plane.
• Plot the coordinate points.
• Then sketch the graph, connecting the points with a line.

Graph :

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.