Linear Transformation Functions

A student graphed f(x) = x and g(x) = f(x + 4). Which statement is true?

• The graph of f is steeper than the graph of g.

• The graph of f is less steep than the graph of g.

• The graph of f is shifted 4 units up to create the graph of g.

• The graph of f is shifted 4 units to the left to create the graph of g.

A student graphed f(x) = x and g(x) = f(x) - 12. Which statement is true?

• The graph of f is shifted 12 units to the right to create the graph of g.

• The graph of f is shifted 12 units down to create the graph of g.

• The graph of f is shifted 12 units up to create the graph of g.

• The graph of f is shifted 12 units to the left to create the graph of g.

What kind of shift happens with this function?

• 4 points up

• 4 points to the left

• 4 points to the right

• 4 points down

Compare the equations f(x) = 12x + 2 and g(x) = 6x – 2. Which best describes the transformation(s) from f(x) to g(x)?

• Vertical shift down 2, less steep slope

• Vertical shift up 4, double the slope

• Vertical shift down 4, half the slope

• Steeper by 2

Given the graph above, which equation shifts line down 5 units?

• y = 4x - 1

• y = 2x - 6

• y = 4x - 6

• y = 2x - 1

In Exercises 1-6, 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 ​​___ translation ​ (a)   units ____ of the graph of f.

• 4

• 2

• 1

• 5

• 6

• 0.5

In Exercises 9-12, use the graphs of f and h to describe the transformation from the graph of f to the graph of h. The graph of h is a (a)   in the _____ of the graph of f.

• reflection

• shrink

• y-axis

• stretch

In Exercises 9-12, use the graphs of f and h to describe the transformation from the graph of f to the graph of h. The graph of h is a _____ in the (a)   of the graph of f.

• reflection

• horizontal

• y-axis

• x-axis

In Exercises 13-18, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. The graph of r is a (a)   _____ of the graph of f by a factor of ____.

• vertical

• down

• up

• horizontal

In Exercises 13-18, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. The graph of r is a _____ (a)   of the graph of f by a factor of ____.

• vertical

• stretch

• shrink

• reflection