Transformations of Graphs of Linear 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.

A student graphed f(x) = x and g(x) = 2f(x). Which statement is true?

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

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

• The graph of f is shifted 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

A student graphed f(x) = x and g(x) = ⅓f(x). 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 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

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.

A student graphed f(x) = x and g(x) = f(x) - ½. 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 ½ unit up to create the graph of g.

• The graph of f is shifted ½ unit down to create the graph of g.

A student graphed f(x) = x and g(x) = 4f(x). 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 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

The function f(x) = x is graphed. A new line is formed by changing the slope to 3 and the y-intercept to -2. Which is true?

• The graph of the new line is steeper and the y-intercept has been translated down.

• The graph of the new line is less steep and the y-intercept has been translated down.

• The graph of the new line is steeper and the y-intercept has been translated up.

• The graph of the new line is less steep and the y-intercept has been translated up.

The function f(x) = x is graphed. A new line is formed by changing the slope to ⅔ and the y-intercept to 15. Which is true?

• The graph of the new line is steeper and the y-intercept has been translated down.

• The graph of the new line is less steep and the y-intercept has been translated down.

• The graph of the new line is steeper and the y-intercept has been translated up.

• The graph of the new line is less steep and the y-intercept has been translated up.

The function f(x) = x is graphed. A new line is formed by changing the slope to ⁴/₃ and the y-intercept to ¹/₃. Which is true?

• The graph of the new line is steeper and the y-intercept has been translated down.

• The graph of the new line is less steep and the y-intercept has been translated down.

• The graph of the new line is steeper and the y-intercept has been translated up.

• The graph of the new line is less steep and the y-intercept has been translated up.