Domain and Range

How to find the range of an absolute value graph

Same thing applied to parabola. To find the vertex, set what is inside the absolute value lines to 0. Solve for x. This is the x value of your vertex. Solve for y. This is the y value.

How to identify if something is a function from an equation

Solve for y and then classify the potential function as a quadratic (x^2 YES), linear graph (mx+b YES), circle (x^2+y^2=r^2 NO), etc.

Sideways Parabola Format

土√x=y (NOT A FUNCTION!)

Vertical line test

A curve (relation) in the coordinate plane is the graph of a function if and only if no vertical line intersects the curve more than once

What is a hyperbola?

A function (f(x)=1/x)

A Function

A relation for which each input has exactly one output. Therefore, the potential function must pass the vertical line test and cannot have repeating domain values to be classified as such.

Polynomials (domain?)

All real numbers

Polynomials with odd degree (domain? range?)

Both all real numbers: ℝ

Piecewise Function

Certain conditions to be met, before rule is applied

f(x)

F at x, declares that at an x point, the f(x) will be a certain value (y value)

How to find the range of a parabola

Find the extremum point! If the extremum is maximum, range is everything less than that. Minimum, range is everything greater than that. Remember, the vertex formula is (-b/2a, f(-b/2a). You can also use the vertex formula and convert using completing the square.

The domain and range are guaranteed to be all real numbers when

The polynomial has an odd degree

Domain

The set of all input values (x values, all real number if it is a polynomial)

Range

The set of all output values

If x is in the denominator

Then x cannot be 0 and y cannot be 0 (y cannot be the reciprocal of answer)