Question

Translate each graph as specified below.(a) The graph of =yfx is shown. Translate it to get the graph of =y+fx2.(b) The graph of =ygx is shown. Translate it to get the graph of =yg−x5.

Answer 1

See graphs below

Step-by-step explanation:
`\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}`

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: