Identifying Functions with Graphs

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 dilation vertical stretch by a factor of 2 of the graph of f

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

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

• Reflection across the origin

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

If the graph of the parent function f(x) = x is a vertical translation shifted 7 units up on the y-axis and is vertically stretched by a factor of 3, what is the function?

• g(x) = 3f(x - 7)

• g(x) = 3f(x) - 7

• g(x) = 3f(x) + 7

• g(x) = 7(x - 3)

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) = 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 parabola opening upwards

• A line with a positive slope

• A curve starting at the origin and increasing slowly

• A hyperbola

• A curve starting at the origin and increasing slowly, shifted down by 1 unit

• A curve starting at the origin and increasing slowly, shifted up by 1 unit

• A curve starting at the origin and increasing slowly, shifted left by 1 unit

• A curve starting at the origin and increasing slowly, shifted right by 1 unit

• A curve starting at the origin and increasing slowly, stretched vertically

• A curve starting at the origin and increasing slowly, compressed vertically

• A curve starting at the origin and increasing slowly, shifted up by 2 units

• A curve starting at the origin and increasing slowly, shifted right by 2 units

• A curve starting at the origin and increasing slowly, shifted left by 3 units

• A curve starting at the origin and increasing slowly, shifted right by 3 units

• A curve starting at the origin and increasing slowly, shifted up by 3 units

• A curve starting at the origin and increasing slowly, shifted down by 3 units