Unit 2 Precalculus

To show an equation has y-axis symmetry

plug in -x for x and get the original equation

To show an equation has x-axis symmetry

plug in -y for y and get the original equation

To show an equation has origin symmetry

plug in -x for x and -y for y and get the original equation

An EVEN function has ___________ symmetry

y-axis

An ODD function has ___________ symmetry

origin

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What type of function is shown? What is the equation?

What transformation is shown? What should be done to the function’s table to create transformation?

shift up, add d to the y-value

What transformation is shown? What should be done to the function’s table to create transformation?

shift down, subtract d from the y-value

What transformation is shown? What should be done to the function’s table to create transformation?

shift left, subtract c from the x-value

What transformation is shown? What should be done to the function’s table to create transformation?

shift right, add c to the x-value

What transformation is shown? What should be done to the function’s table to create transformation?

vertical stretch, multiply the y-value by a

What transformation is shown? What should be done to the function’s table to create transformation?

vertical compression, multiply the y-value by a

What transformation is shown? What should be done to the function’s table to create transformation?

horizontal stretch, divide the x-value by b (multiply by reciprocal)

What transformation is shown? What should be done to the function’s table to create transformation?

horizontal compression, divide the x-value by b

What transformation is shown? What should be done to the function’s table to create transformation?

reflection over y-axis, divide x by b

What transformation is shown? What should be done to the function’s table to create transformation?

reflection over x-axis, multiply y by a

Definition of a FUNCTION

every x-value only maps to ONE y-value

To determine a graph is a function

vertical line test. If a vertical line passes the graph no more than one point at any point on the graph it is a function.

To determine if an equation is a function

solve for y and plug in a value for x. If each x-value results in only one y-value, then it is a function.