See graphs below
Explanation:[tex]\begin{gathered} a)\text{ y = f(x)} \\ f(x)\text{ + 2 is a translation of 2 units upward} \\ To\text{ get }y\text{ = f(x )+ 2, we will assign values to x and add 2 to its y coordinates in order to get } \\ \text{the coordinates of the new one} \end{gathered}[/tex]
let x = -2, -1, 0, 1, 2
on the original
when x = -2, y = -3
new y coordinate = -3 + 2 = -1
when x = -1, y = 0.5
new y -coordinate = 0.5 + 2 = 2.5
when x = 0, y = 1
new y coordinate = 1 + 2 = 3
when x = 1, y = 1.5
new y oordinate = 1.5 +2 = 3.5
when x = 2, y = 5
new y-coordinate = 5 + 2 = 7
plotting the new points against x:
b) y = g(x)
y = g(x - 5)
subtract 5 from the x coordinate of the previous line
We will assign values for x, in order to get values of y
let x = 0, 1, 3
when x = 0, y = 0
new x coordinate = 0 - 5 = -5
when x = 1, y = 4
new x coordinate = 1 - 5 = -4
when x = 3, y = 7
new x coordinate = 3 - 5 = -2
plotting the points on the graph:
