The graph of y = f x , where - 3 ≤ x ≤ 6 , is shown. Copy the graph of f and draw the function g ( x ) = 3 f ( x ) on the same axes.

The graph of y = f x , where - 3 ≤ x ≤ 6 . We want to draw the function g ( x ) = 3 f ( x ) on the same axes. We know that if y = a f x then there is vertical stretch for a > 1 . Here a = 3 ⇒ vertical stretch with scale factor 3 . Each point on the graph g x = 3 f x is 3 times the distance to the x - axis as the corresponding point on the graph of g x = f x .

The graph of y = f x , where - 3 ≤ x ≤ 6 , is shown. Copy the graph of f and draw the function g ( x ) = 3 f ( x ) on the same axes.

The graph of y = f x , where - 3 ≤ x ≤ 6 . We want to draw the function g ( x ) = 3 f ( x ) on the same axes. We know that if y = a f x then there is vertical stretch for a > 1 . Here a = 3 ⇒ vertical stretch with scale factor 3 . Each point on the graph g x = 3 f x is 3 times the distance to the x - axis as the corresponding point on the graph of g x = f x .

The graph of y = f x , where - 3 ≤ x ≤ 6 , is shown. Copy the graph of f and draw the function g ( x ) = f ( x + 6 ) on the same axes.

The graph of y = f x , where - 3 ≤ x ≤ 6 . We want to draw the function g ( x ) = f ( x + 6 ) on the same axes. We know that if y = f ( x − h ) then the graph is translated to the left h units for h < 0 . Now, g x = f x + 6 = f x - - 6 . So, the graph is translated to the left by 6 units.

The graph of y = f x , where - 3 ≤ x ≤ 6 , is shown. Copy the graph of f and draw the function g ( x ) = f ( x ) − 3 on the same axes.

The graph of y = f x , where - 3 ≤ x ≤ 6 . We want to draw the function g ( x ) = f x - 3 on the same axes. We know that if y = f x + k then the graph is translated downwards by k units for k < 0 . Here, g x = f x - 3 = f x + - 3 . So, graph is translated downwards by 3 units.