Question

Hori‖ Transf Sullivan Guided Vis Q3 Use the guided visualization to answer the question. Click here to open the guided visualization. a) If y=f(x) is some function whose graph contains the point (2,4), the graph of y = f(x – 3) would contain the point b) If y = f(x) is some function whose graph contains the point (3,2), the graph of y=f(x + 5) would contain the point a) The graph of y = f(x-3) contains the point (0,0). (Type an ordered pair.)

Answer 1

Answer:

a) If y=f(x) is some function whose graph contains the point (2,4), the graph of y = f(x – 3) would contain the point (2, 1)

b) If y = f(x) is some function whose graph contains the point (3,2), the graph of y=f(x + 5) would contain the point (3, 64)

Explanations:

The function represented by the graph given is:

y = f(x) = x²

a) If the graph of y = x² contains the point (2, 4):

x = 2, y = 4

to get y = f(x - 3), change x in y = x² to x-3

Therefore, y = f(x-3) = (x - 3) ²

Get the value of y at x = 2, using the new equation for y:

y = (x - 3)²

y = (2 - 3)²

y = (-1)²

y = 1

Therefore, the graph of y = f(x - 3) will contain the point (2, 1)

b)

If the graph of y = x² contains the point (3, 2):

x = 3, y = 2

to get y = f(x + 5), change x in y = x² to x+5

Therefore, y = f(x+5) = (x + 5) ²

Get the value of y at x = 3, using the new equation for y:

y = (x + 5) ²

y = (3 + 5) ²

y = 8²

y = 64

Therefore, the graph of y = f(x - 3) will contain the point (3, 64)