Function Vocab
the values you put in a function
the INPUT
Evaluate f(x)=-3x if x=2
What is -6?
how does the graph of the absolute value function shift if the expression is |x-3|
3 units to the RIGHT
find the inverse function of f(x)=-3x
x=f(x)/-3
how do you determine if a function is piecewise?
if the rule to determine the output changes depending on the input
the value you get out of a function
The OUTPUT
Evaluate f(x)=2x+1 if x=-2
What is -3?
what is the equation of an absolute value function shifted UP 6 units?
y=|x|+6
find the inverse of f(x)=2x+1
x= (f(x)-1)/2
graph the function
f(x)={3x, 0<=x<=3}
{x-2, 3<x<=8}
See Graph on desmos
The DOMAIN
Evaluate f(x)=-3 - 2x if x=6
What is -15?
write the equation graphed (view PIC 1)
y=|x+4|
find the inverse of f(x)=-3 - 2x
x= (f(x)+3)/-2
graph the function
f(x)= {2, -5≤x≤1}
{x, 1<x≤5}
{7, 5<x≤7}
the set of all possible outputs of a function
The RANGE
Evaluate f(x)=25 + 4x if x=5
What is 45?
write the equation of the graph (view PIC 2)
y=|x|-2
what is the inverse of f(x)=25 + 4x
x= (f(x)-25)/4
f(x)= {-5, -10<x<-5}
{x, -5≤x<0}
{1, 0≤x<3}
{x-2, 3≤x<8}
{6, 8≤x<10}
What do f(-1),f(5), and f(9) equal?
f(-1)=-1, f(5)=3, f(9)=6
A relation where each input has one and only one output
A FUNCTION
Evaluate f(x)=-(4x+2) if x=7
What is -30
write the equation graphed (view PIC 3)
y=|x-2|+3
find the inverse function of f(x)=-(4x+2)
x= (-f(x)-2)/4
A glass of liquid starts at 65 degrees and increased by 2 degrees each minute, then after 5 minutes, ice is put into the liquid. The ice immediately cools the liquid down to 50 degrees. the liquid continues cooling down 1 degree a minute for 3 minutes
Write the function where F(x) represents the temperature of the liquid, and x represents the amount of minutes that have passed
F(x)={65+2x, 0<=x<=5}
{55-x, 5<x<=8 }