Transforming Functions with function notation af(b(x-c))+d

Matching Match the change in the function on the left to the transformation on the right f(x + c) shift left f(x - c) shift right f(x) + d shift up f(x) - d shift down Matching Match the change in the function on the left to the transformation on the right -f(x) reflects over x-axis af(x) --> when a>1 vertical stretch af(x) --> when 0 b>1 horizontal compression f(b(x)) -> 0 How does the graph of f(x)=√x compare to the graph of g(x)= f(x)-3? vertically translates up 3 units horizontally translates right 3 units vertically translates down 3 units horizontally translates left 3 units How does the graph of f(x)=x3 compare to the graph of g(x) = f(x-1)? vertically translates up 1 unit horizontally translates right 1 unit vertically translates down 1 unit horizontally translates left 1 unit How does the graph of f(x)=1 compare to the graph of g(x)=4f(x)? vertical compression by a factor of 1 vertical stretch by a factor of 4 horizontal stretch by a factor of 4 horizontal compression by a factor of 1 How does the graph of f(x)=|x| compare to the graph of g(x)=f(x+4)? vertically translates up 4 units horizontally translates right 4 units vertically translates down 4 units horizontally translates left 4 units How does the graph of f(x)=√x compare to the graph of g(x)= f( 1 horizontal stretch by a factor of 5 vertical stretch by a factor of 5 horizontal compression by a factor of 1 vertical compression by a factor of 1 How does the graph of -f(x) compare to the graph of f(x)? shifts it down reflected over the y-axis reflected over the x-axis compresses it How does the graph of f(-x) compare to the graph of f(x)=x2? shifts it down reflected over the y-axis reflected over the x-axis horizontal compression How does the graph of f(x)=log(x) compare to the graph of g(x)=f(x)+6? vertically translates up 6 units horizontally translates right 6 units vertically translates down 6 units horizontally translates left 6 units 1How does the graph of f(x)=√x compare to the graph of g(x)= 1 f(x)? horizontal stretch by a factor of 2 vertical stretch by a factor of 2 horizontal compression by a factor of1 vertical compression by a factor of1 How does the graph of f(x)=2x compare to the graph of g(x)=f(3x)? vertical compression by a factor of 1 vertical stretch by a factor of 3 horizontal stretch by a factor of 3 horizontal compression by a factor of 1 In the following picture, the red graph, g(x), represents a transformation of the parent function, f(x)=x3, in black. Choose the function notation that represents the red graph. g(x) = f(x) + 3 g(x) = f(x) -3 g(x) = f(x + 3) g(x) = f(x -3) In the following picture, the red graph, g(x), represents a transformation of the parent function, f(x)=|x|, in black. Choose the equation that most likely represents the red graph. g(x) = f(x) + 2 g(x) = f(x) - 2 g(x) = f(x+ 2) g(x) = f(x -2) Determine all the ways that the graph of g(x) = -3f(x) +5 would differ from the graph of f(x) = x2. Check all that apply. Reflected over the x-axis Vertically Stretched by 3 Vertically Compressed by 1 Shifted Up 3 Reflected over the y-axis Shifted up 5 Shifted down 5 Shifted right 5 Shifted left 5 Shifted right 3 Shifted left 3 Shifted down 3 Determine all the ways that the graph of g(x) = 0.5f(x - 3) + 2 would differ from the graph of f(x) = |x|. Check all that apply. Reflected over the x-axis Vertically Stretched by 0.5 Vertically Compressed by 0.5 Shifted Up 3 Reflected over the y-axis Shifted up 2 Shifted down 2 Shifted right 2 Shifted left 2 Shifted right 3 Shifted left 3 Shifted down 3 horizontal stretch by .5 horizontal compression by .5 Describe all the ways that the graph of g(x) = -2f(x + 4) - 6 would differ from the graph of f(x) = x3. reflected over the x-axis reflected over the y-axis vertically stretched by 2 vertically compressed by 2 shifted right 4 shifted left 4 shifted down 6 shifted up 6 horizontal stretch by 2 horizontal compression by 2 Describe all the ways that the graph of g(x) = .75f(x - 2) + 1 would differ from the graph of f(x) = x2. reflection over the x-axis vertical compression by .75 vertical stretch by .75 shifted left 2 shifted right 2 shifted down 2 shifted up 2 shifted down 1 shifted up 1 shifted left 1 shifted right 1 horizontal stretch by .75 horizontal compression by .75 Describe all the ways that the graph of g(x) = f(2x) + 5 would differ from the graph of f(x) = x4. reflection over the x-axis vertical stretch by 2 horizontal compression by 1 vertical compression by 1 horizontal stretch by 2 shifted up 5 shifted down 5 shifted left 5 shifted right 5 Describe all the ways that the graph of g(x) = f(1 x) -9 would differ from the graph of f(x) = |x|. reflection over the x-axis vertical stretch by 3 horizontal compression by 1 vertical compression by 1 horizontal stretch by 3 shifted up 9 shifted down 9 shifted left 9 shifted right 9