Transformation of Linear Function

A student graphed f(x) = x and g(x) = f(x - 15). Which statement is true?

• The graph of f is shifted 15 units to the right to create the graph of g.

• The graph of f is shifted 15 units down to create the graph of g.

• The graph of f is shifted 15 units up to create the graph of g.

• The graph of f is shifted 15 units to the left to create the graph of g.

Which transformation will occur if f(x) = x is replaced with 2f(x)?

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units

• Translation right 2 units

• Vertical translation up by 2 units.

• Reflection across the x-axis.

Which transformation on f(x) = x is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Rewrite f(x) = 2x - 1 shifted up three units and the slope doubled (a)  

• f(x) = 5x - 2

• f(x) = 4x + 2

• f(x) = 4x + 3

• f(x) = 5x - 4

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation. (a)  

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

• down

• up

• right

• left

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 3. Describe the transformation. (a)  

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically