Chapter 1 Summative Review: Symmetry Tests, Even/Odd Functions, Inverse Functions

If a graph is Symmetric With Respect to the X-axis, and the point (X, Y) is a solution to the equation, then the point (____, ____) will also be a solution to the equation.

(X, -Y)

If a graph is Symmetric With Respect to the Y-axis, and the point (X, Y) is a solution to the equation, then the point (____, ____) will also be a solution to the equation.

(-X, Y)

If a graph is Symmetric With Respect to the Origin,

and the point (X, Y) is a solution to the equation,

then the point (____, ____) will also be a solution to the equation.

(-X, -Y)

If a graph of a function is Symmetric With Respect to the X-axis, then the function is (EVEN / ODD / NEITHER)

NEITHER

If a graph of a function is Symmetric With Respect to the Y-axis,

then the function is (EVEN / ODD / NEITHER)

EVEN

If a graph of a function is Symmetric With Respect to the Origin,

then the function is (EVEN / ODD / NEITHER)

ODD

If a function is ODD, then f(-x) =

-f(x)

If a function is EVEN, then f(-x) =

f(x)

The real ZEROS of a function can be identified by locating the ______________________ of the graph.

x-intercepts

To find the real ZEROS of a function algebraically, "Let _____ = ______" and solve for x (FACTOR!)

Let f(x) = 0

To find the Y-INTERCEPTS of a function algebraically, "Let _____ = ______" and solve for y.

Let x = 0

To find the Y-INTERCEPTS of a function, find --

f(0)

To find the ZEROS of a function, find the values of x that make f(x) =

0

This test confirms that a graph IS a function.

Vertical Line Test

This test confirms that the INVERSE of a function will ALSO be a function.

Horizontal Line Test

If a FUNCTION passes through the point (X, Y), then the INVERSE of the function will pass through the point (____, ____)

(Y, X)

To find the equation for the INVERSE of function f(x) -- (1) Replace f(x) with ____, (2) Swap ____'s and ____'s, (3) Solve for (isolate) ____, (4) Replace y with ____.

(1) y

(2) x's and y's

(3) y

(4) f^-1(x)

If a FUNCTION is graphed in the same coordinate plane as its INVERSE, the two graphs should be Symmetric With Respect to the line --

Y = X

If a function is ODD, its graph will exhibit Symmetry With Respect to the --

ORIGIN

If a function is EVEN, its graph will exhibit Symmetry With Respect to the --

Y-AXIS