MATH 100 - MIDTERM 1 CONTENT
Vertical shifts - Answers -f(x) + c shift up
f(x) - c shift down
Vertical scaling - Answers -bf(x) expand vertically
1/bf(x) contract vertically
Vertical flip - Answers --f(x) flip about the x-axis
Horizontal shift - Answers -f(x-c) shift right
f(x+c) shift left
Horizontal scaling - Answers -f(1/bx) expand horizontally
f(bx) contract horizontally
Horizontal flip - Answers -f(-x)
even and odd functions - Answers -Odd function: f(-x) = f(x) [i.e. x^2 when x = -x]
Even function: f(-x) = -f(x) [i.e. x^3 when x= -x]
Neither: when it is not the same or opposite of original function when substituting a
negative value
How to tell even or odd graphs - Answers -When the function has rotation symmetry
(can be rotated upside down and be the same) but is not centred on the y-axis = odd
function
When the function is symmetrical (on y-axis) = even function
f compose g (fog) - Answers -Take f(x), the outside function
Replace every instance of x with g(x), the inside function
What makes a function invertible - Answers -it must be one-to-one and can be
determined with a horizontal line test
Properties of inverse functions - Answers -if f(x) = y then x = f^-1(y)
f(x)=y <--> f^-1(y)=x
Composing a function and its inverse cancels each other out leaving you with either x or
y
Inverses switch the domain and range with one another
what was x is now y and what was y is now x
Slope formula - Answers -y2-y1/x2-x1
Vertical shifts - Answers -f(x) + c shift up
f(x) - c shift down
Vertical scaling - Answers -bf(x) expand vertically
1/bf(x) contract vertically
Vertical flip - Answers --f(x) flip about the x-axis
Horizontal shift - Answers -f(x-c) shift right
f(x+c) shift left
Horizontal scaling - Answers -f(1/bx) expand horizontally
f(bx) contract horizontally
Horizontal flip - Answers -f(-x)
even and odd functions - Answers -Odd function: f(-x) = f(x) [i.e. x^2 when x = -x]
Even function: f(-x) = -f(x) [i.e. x^3 when x= -x]
Neither: when it is not the same or opposite of original function when substituting a
negative value
How to tell even or odd graphs - Answers -When the function has rotation symmetry
(can be rotated upside down and be the same) but is not centred on the y-axis = odd
function
When the function is symmetrical (on y-axis) = even function
f compose g (fog) - Answers -Take f(x), the outside function
Replace every instance of x with g(x), the inside function
What makes a function invertible - Answers -it must be one-to-one and can be
determined with a horizontal line test
Properties of inverse functions - Answers -if f(x) = y then x = f^-1(y)
f(x)=y <--> f^-1(y)=x
Composing a function and its inverse cancels each other out leaving you with either x or
y
Inverses switch the domain and range with one another
what was x is now y and what was y is now x
Slope formula - Answers -y2-y1/x2-x1
