Function Vocabulary
The set of all possible inputs of a function
The domain
Does a straight line represent a function ?
Yes ! Except if it is perfectly vertical.
The general form of a linear function?
y=mx+b
If f(x)=2x+3,
find f(1).
f(1)=5
If the curve goes up, the function is…
Increasing
The set of all outputs of a function
The range
The rule used to determine if a graph represents a function.
The vertical line test
The name of m in y=mx+b ?
The slope
f f(x)=3x+2,
find f(2.5)
f(2.5)=9.5
If the curve goes down when x increases, the function is…
Decreasing
Read "f(x)=y" in English
f of x equals y
Do the ordered pairs (1,3),(2,5),(3,7) represent a function ?
Yes
The name of b in y=mx+b ?
The y-intercept
If f(x)=4x−1,
find f(3/4)
f(3/4)=2
If all outputs of a function are greater than 0, the function is…
Positive
In a function, each input corresponds to…
Exactly one output
Do the ordered pairs (1,3),(1,5),(2,4) represent a function ?
How can we determine if a linear function is increasing or decreasing without its graph ?
Look at the sign of the slope m:
m>0 → increasing
m<0 → decreasing
If f(x)=7−3x,
simplify f(x+2)
f(x+2)=7−3(x+2)=1−3x
The point where a line crosses the y-axis is called…
The y-intercept
The definition of a function in mathematics
A function is a rule that relates one set to another set and assigns exactly one output to each input.
Give an example of a relation that is not a function.
y2=x, ou y2+x2=1
Visually, what happens to the line when we change the value of m ? of b ?
👉 Changing m rotates the line.
👉 Changing b shifts the line up or down.
If f(x)=x2+3x−1,
simplify f(x+h)
f(x+h)=(x+h)2+3(x+h)−1
=x2+2xh+h2+3x+3h−1
What is the difference between English and French when we say that a number/function is positive ?
In French: positive means ≥0
In English: positive means >0