Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6? a. left 1 unit, up 5 units b. right 1 unit, up 5 units c. left 2 units, up 2 units d. right 2 units, up 2 units

The correct option is A.

Step-by-step explanation:

The given functions are,

To make perfect square add and subtract , where a is coefficient of leading term and b is the coefficient of middle term.

Therefore add and subtract 1.

The function is in the form of

Where a shows horizontal shift and b shows vertical shift. If a>0, then the graph of f(x) shifts left side by a units and  if a<0, then the graph of f(x) shifts right side by a units.

If b>0, then the graph of f(x) shifts upward by b units and if b<0, then the graph of f(x) shifts downward by b units.

Sicen the value of a is 1 and value of b is 5, therefore the graph of f(x) shifts 1 unit left and 5 unit upward. The option A is correct.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.