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)