Transformations of Functions
what is an equation for a quadratic function shifted down by 2?
f(x)=x2-2
which of the following functions will increase faster?
f(x)=4*5x
h(x)=4*6x
h(x)
What is the formula for the Pythagorean Theorem?
a2+b2=c2
cos(120)=
-1/2
How do we call the inverse of cosine?
arccosine
what is an function for a quadratic equation with a vertical stretch of 2 and a horizontal shift right 3?
f(x)=2(x-3)2
log10(10)+log2(32)=
6
What is the formula for Law of Sine?
sin(A)/a = sin(B)/b = sin(C)/c
tan(135)=
-1
What is the inverse function of ln(x)?
f(x)=ex
what is an equation for the absolute value function shifted to the left by 20?
f(x)=|x+20|
log4(8)+log4(32)=
4
What is the formula for Law of Cosine?
c2=a2+b2-2ab Cos(C)
arccos(-1)
pie
Find the inverse of f(x)=3x-4
f-1(x)=x/3+4/3
what is an equation for the quadratic function shifted up by 5, to the right by 4, and reflected across the x-axis?
f(x)= - (x-4)2-5
The function f is given by f(x)=9*25x. Which of the following is an equivalent form for f(x)?
A. f(x)=3*5(x/2)
B. f(x)=3*5(2x)
C. f(x)=9*5(x/2)
D. f(x)=9*5(2x)
D. f(x)=9*5(2x)
What is the standard form for a linear equation?
ax+by=c
arctan(1)=
pie/4
what is the axis of symmetry between a function and its inverse function?
y=x
f(x)= - 4(x+5)2-2
Which of the following is equivalent to 2(lnx) - 3ln(y) ?
A. ln(x2/y3)
B. ln(x2y3)
C. ln(2x-3y)
D. ln(2x/3y)
A. ln(x2/y3)
What is the inverse function property?
f(f-1(x))=x
f-1(f(x))=x
arcsin(1)+arccos(0)
pie
Describe how to find the inverse function of f(x) in words.
(1) set function f(x) = y
(2) write x in terms of y (solve for x)
(3) switch x and y (interchange the variables)