UTMA REVIEW WITH COMPLETE SOLUTIONS
100% 2023/2024
even function
>symmetric about y-axis
> f(-x) = f(x)
odd function
>symmetric through a line through origin
> f(-x)=-f(x)
domain of f(g(x))
>x-values in domain of g
>x-values that make g(x) in domain of f
what does an inverse function do
flips graph over y=x
to test if two functions are inverses
f-1(f(x)) = x
f(f-1(x)) = x
(plug inverse into f and plug f into inverse, must get x)
to find an inverse
switch x and y
to test if a function has an inverse
horizontal line test (does not have an inverse if a horizontal line intersects the graph at more than
point "1 to 1"
does an inverse exist for y = +/- radical x
no because two y values for every x- value
what is the HA?
BOBO BOTN EATS DC
to find slant asymptote
do long division and ignore remainder
rewrite f(x)=|2x-3| in piece-wise way
2x-3 if x greater than or equal to 3/2
-2x+3 if x is less than 3/2
a^x when x=0
1
100% 2023/2024
even function
>symmetric about y-axis
> f(-x) = f(x)
odd function
>symmetric through a line through origin
> f(-x)=-f(x)
domain of f(g(x))
>x-values in domain of g
>x-values that make g(x) in domain of f
what does an inverse function do
flips graph over y=x
to test if two functions are inverses
f-1(f(x)) = x
f(f-1(x)) = x
(plug inverse into f and plug f into inverse, must get x)
to find an inverse
switch x and y
to test if a function has an inverse
horizontal line test (does not have an inverse if a horizontal line intersects the graph at more than
point "1 to 1"
does an inverse exist for y = +/- radical x
no because two y values for every x- value
what is the HA?
BOBO BOTN EATS DC
to find slant asymptote
do long division and ignore remainder
rewrite f(x)=|2x-3| in piece-wise way
2x-3 if x greater than or equal to 3/2
-2x+3 if x is less than 3/2
a^x when x=0
1
