Introduction to functions Flashcards
What is a function?
A rule to assign an input to an unique output value
The input is called the:
independent quantity
The output is called the:
dependent quantity
In math, functions are usually represented by the letter:
f (sometimes g or h)
Create a situation and provide a function.
f(x) = 0.18x
Where 18% is the gratuity and x is the cost of the meal.
Is the equation x + y = 2 of function? Why/ why not?
It is!
Is the equation x² + y² = 9 a function? Why/ why not?
It is not! A function only spits out ONE output for a given input.
What is the vertical line test?
A test to help us see if a curve is a function by evaluating if a vertical line intersects the curve at MOST once.
What is a One-to-one function?
If one output value is associated with EXACTLY one input value.
Is this function one-to-one?
No, because because the output y has more than one input value x.
If f(2) = 2² = 4
If f(-2) = -2² = 4
What is the horizontal line test?
A function is one-to-one if the horizontal line intersects the curve at most ONCE.
Let f(x) = 2x² -2x
What is f(x) = 24
x = 4 or x = - 3
Let f(x) = 2x² -2x.
Simplify
Answer: 2h - 18
What is the domain of a function?
Set of all possible inputs denoted as Dsubf or dom(f)
What is the range of a function?
Set of all possible outputs. Rsubf or ran(f)
What is the domain of this function?
All real numbers
What is the range of this function?
0 to infinity
What would be the domain and range of this function?
dom(f) =
ran(f) =
Since you cannot do the square negative values:
What would be the domain and range of this function?
dom(f) =
ran(f) =
What is the domain and range of this function?
f(x) = ∛x
All values of x are defined since:
If n is an even number ( n = 2, 4, 6, …) then the domain of f(x) = n√x is:
If n is an odd number ( n = 1, 3, 5, …) then the domain of f(x) = n√x is:
R: all real numbers
The domain of ANY polynomial (variables with positive integer exponents) is:
R: all real numbers
What is the first idea to find the domain of a function?
Give an example in terms of A/B.
The fraction A/B is defined only if B ≠ 0
What is the second idea to find the domain of a function?
Give an example in terms of √A.
Find the domain (set of all x) of this function.
Use the first idea to find the domain in this situation:
Find the domain (set of all x) of this function.
Use the first idea to find the domain in this situation:
What is a piecewise function?
It is a function where different formulas are use depending on the input.
What would be the piecewise function of this example:
A monthly phone plan costs $25 per month for up to 1000 minutes and charges $0.05 for each additional minute.
What is the absolute value function?
Most popular piecewise function.
States that if a value is greater or at 0 then the absolute value is the same. If the number is lower than zero you add a - to make it positive.
What is considered a symmetric y-axis curve?
If its reflection in the y-axis is the same as the original graph.
What is an even function?
A function is an even function if f(x) is equal to f(−x) for all the values of x. Its graph is symmetric with respect to the
y-axis
What is considered a symmetric x-axis curve?
If its reflection in the x-axis is the same as the original graph. (none of them are functions though)
What is considered a symmetric origin curve?
If its reflection over BOTH axes is the same as the original graph.
If replacing x with -x and y with -y gives you the same equation then the curve is symmetric about the origin.
What is an odd function?
The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x).
x not equal to -2
x ≥ 0
Is this f function even, odd, or neither?
odd
Neither
Neither
He made a mistake in step 1.
Even
Neither
odd
Tamara’s work is correct.
f(2) DNE
y-intercepts: 3, -3
x-intercept: -9
Symmetric on x-axis
Symmetric on the origin
What is the domain of this function? (interval notation)
(-infinity,-3)U(-3,3)U(3,infinity)
What is the domain of this function? (interval notation)
(-9/16,infinity)
A = -1
B = 6
domain of f(x) = (-infinity,0]U[5,infinity)
domain of g(x) = R
f(-6) =
f(-1) =
f(7) =
f(-6) = 24
f(-1) = -1
f(7) = 12
q(0.02) = 727/25
Graph:
Answer: D
Domaine: (-infinity, infinity)
Range: (-infinity,6)
