1 Functions Flashcards
Which are NOT rules for functions Y=x^2 + 3 Y^2 - x^2 =0 Y = sqrt(x +3) Y^3 = x Y^4 = x
Y^4 = x
Y^2 - x^2 =0
A function must have
One output exactly
Domain
Set of input values
Domain of y = sqrt(x)
X can’t be a negative
Therefore the domain must me x ≥ 0
What is the rule
The function equation
Set of all the real numbers
×∈ℝ
Domain for 1/ (t-2)
×∈ℝ, t ⊧2
F(3) = 9 with arrows
F:3 → 9
Many-one functions
Two or more inputs that give the same output
If a function is not a many-one function, it must be a
One-one function
If the function is < or > rather than ≤ or ≥ then the graph must have
An empty cycle on the end where the graph breaks
The range
The complete set of possible output values
How to find the range (2 options)
Complete the square, the number on the end (c)
F(x) ≥ c
Find the x value extremities, find what y value they give
Write in a < f(x) < 9
Range of g(t) = 3^t
G(t) > 0
Range of f(x) = 1/x -5. X⊧0
F(x) = x∈ℝ, f ⊧ -5
Generally finding the range
Put in minimum value that is often the maximum range
0 < f(x) < (minimum value)
Or
0 < f(x) ≤ (minimum value)
The second sign depends on what it is in the domain
What do many-one functions not have
NO INVERSE FUNCTIONS
Why might there not be an inverse function?
ITS A MANY-ONE
Domain of F^-1 (x)
=range of f(x)
How to draw the inverse function
Draw function
Then reflect in y=x
