Transformations Algebra

Write a function g whose graph represents the indicated transformation of the graph of f.

f\left(x\right)=-3\left|x-4\right|, vertical shrink by a factor of\frac{1}{2}

Does the following shift up or shift down from the parent function y = |x|?
y = |x| - 8

• Shift up

• Shift down

Does the following get wider  or skinnier from the parent function y = |x|?
y = 5|x| 

• Wider

• Skinnier

Choose the correct translated function.

• f(x)= |x|+2

• f(x)= |x|-2

• f(x)= -|x|

• f(x)= -|x|+2

• Function 2's graph is shifted down 8 units from Function 1's graph.

• Function 2's graph is shifted up 8 units from Function 1's graph.

• Function 2's graph is shifted left 8 units from Function 1's graph.

• Function 2's graph is shifted right 8 units from Function 1's graph.

• Function 2's graph is LESS steep (wider) than Function 1's graph and IS reflected.

• Function 2's graph is MORE steep (narrower) than Function 1's graph and IS reflected.

• Function 2's graph is LESS steep (wider) than Function 1's graph and is NOT reflected.

• Function 2's graph is MORE steep (narrower) than Function 1's graph and is NOT reflected.

How did we transform from the parent function?

y = -1/5x² + 7 (Choose ALL that apply.)

• reflection over the x-axis

• vertical shift up 7

• vertical stretch of 1/5

• vertical shift down 7

• vertical compression of 1/5

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of f is a horizontal translation two units left of g

• The graph of g is a vertical stretch by a factor of 2 of the graph of f

• The graph of g is a reflection of the graph of f

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 4 units up from the graph f

• The graph of g is a horizontal translation of the graph of f, 4 units right

• The graph of g is a horizontal translation of the graph of f, 4 units left

• The graph of g is a vertical stretch of the graph of f, by a factor of 7

How does the graph of g(x) compare to f(x)?

• g(x) is steeper and shifted down from f(x)

• g(x) is steeper and shifted up from f(x)

• g(x) is flatter and shifted down from f(x)

• g(x) is flatter and shifted up from f(x)