Transformation of Functions

The vertex of the quadratic function f(x) in the picture (2, -2). If g(x) = f(x) - 4, what is the vertex of g(x)?

• (2, -6)

• (2, 2)

• (-2, -2)

• (6, -2)

• Compresses closer/ More narrow

• Gets wider 

• Shifts up

• Shifts down

• Graph gets narrow

• Graph gets wider

• Graph shifts to the left

• Graph shifts to the right

If the original function is f(x), how will f(x-t) + s transform f(x)?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

If the original function is f(x), how will -f(x) transform f(x)?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

If the original function is f(x), how will f(-x) transform f(x)?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

If the original function is f(x), how will af(x) transform f(x)?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

If the original function is f(x), how will f(ax) transform f(x)?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

f(x) = x+2 and g(x) = 2x + 4 . What transformation happened?

• One way stretch, parallel to x-axis, with scale factor 1/2

• One way stretch, parallel to y-axis, with scale factor 2

• Translation of f(x) with vector (2 , 1)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis

f(x) = 6x -x^2  and g(x) = x^2 - 6x. What transformation happened?

• One way stretch, parallel to x-axis, with scale factor 1/a

• One way stretch, parallel to y-axis, with scale factor a

• Translation of f(x) with vector (t , s)

• Reflection of f(x) in the x-axis

• Reflection of f(x) in the y-axis