Precalculus homework help.

Question

Write the equation of a sine function that has the given characteristics.

1.The graph of y = x2, shifted 2 units downward.

2.The graph of y = x , shifted 6 units to the right.

Answer 1

For both of these, remember that whatever is in parentheses with the x moves the function in the opposite direction of its sign. y=(x-3)² would move Right three units. Whatever's not stuck in with the x moves the y values. Adding and subtracting move the function up and down. Multiplying the x values by something >1 stretches out the function ("vertical stretch") or, if the coefficient is less than one, squishes the whole function down. ("vertical compression"). To shift y=x² down two, simply subtract two: y=x²-2.

To move y=x six units to the right, SUBTRACT 6 from x: y=x - 6. (In the case of the linear function, this also moves it down 6.)

I hope that helps!

Have fun mathing, and don't hesitate to reach out if you have any questions!

Liz Z.