Algebra Unit 5 Special Functions Test Part 1 Vocab

Relation : Any set of ordered pairs

Input : The "x" value in a set of data on which a function operates. It is the domain.

Function Notation : An equation in the form of 'f(x)=' to show the output value of a function, f, for an input value, x

How do you find the vertex of an absolute value function? : Set the values in the absolute value equal to zero and solve for the x value of the vertex. The y value of the vertex is the number on the end.For example: y=2|x+4|-3Vertex: (-4,-3)

Point of Discontinuity : A point in the graph of a function where the graph does not exist. There is a hole there.

Vertical Asymptote : Zeros in the denominator that do not make the numerator equal to zero. These factors do not cancel.

If the degree of the numerator is equal to the degree of the denominator : The rational function has one horizontal asymptote at y=a/b, where a is the coefficient of the leading term in the numerator and b is the coefficient of the leading term in the denominator

How do you find the points of discontinuity? : Look at the factored form and find all values that make the denominator equal to zeroIf the factor cancels: holeIf the factor does not cancel: vertical asymptote

How do you find x intercepts? : Set y equal to zero and solve for the x value(s)

How do you find a y intercept? : Set x equal to zero and solve for y

Inverse Function : A function that "undoes" what the original function does. It does the inverse operations in the reverse order to get back to the number that the original function started with.

How do you find an inverse function? : Switch x and y and solve for y1. Rewrite the equation using "y"2. Interchange x and y3. Solve for y4. Decide if the inverse is a function

Quadratic Function : f(x)=a(x-h)^2+k

Square Root Function : f(x)=a√(x-h) +k

Square root functions: Positive a value : Points up

Square root functions: Negative a value : Points down