Math 110 Exam Review
How do you know if a function is odd? - Answers -f(-x) = -f(x)
ex. f(x)=x^3
f(-x)=-x^3
How do you know if a function is even? - Answers -f(-x)=f(x)
ex. f(x)=x^2
f(-x)=x^2
f(x)=(x-c)
What kind of transformation is this? - Answers -horizontal shift
f(x)=x-c
What kind of transformation is this? - Answers -vertical shift
f(x)=ax when a>1
What kind of transformation is this? - Answers -vertical stretch
f(x)=ax when a<1
What kind of transformation is this? - Answers -vertical compression
f(x)=sin(ax) when a>1
What kind of transformation is this? - Answers -horizontal compression
f(x)=sin(ax) when a<1
What kind of transformation is this? - Answers -horizontal stretch
f(x)=(-x)^2
What kind of transformation is this? - Answers -reflection over the x-axis
f(x)=-x^2
What kind of transformation is this? - Answers -reflection over the y-axis
f(x)=a(x-h)^2 +k
What is this called? - Answers -vertex form of a quadratic
What is the domain for composition functions when they are sums, differences, or
products? f(g(x)) - Answers -Where f(x) and g(x) overlap
What is the domain for composition functions when it is a quotient? f(g(x)) - Answers -
where f(x) and g(x) overlap EXCEPT where g(x)=0
How do you know if a function is odd? - Answers -f(-x) = -f(x)
ex. f(x)=x^3
f(-x)=-x^3
How do you know if a function is even? - Answers -f(-x)=f(x)
ex. f(x)=x^2
f(-x)=x^2
f(x)=(x-c)
What kind of transformation is this? - Answers -horizontal shift
f(x)=x-c
What kind of transformation is this? - Answers -vertical shift
f(x)=ax when a>1
What kind of transformation is this? - Answers -vertical stretch
f(x)=ax when a<1
What kind of transformation is this? - Answers -vertical compression
f(x)=sin(ax) when a>1
What kind of transformation is this? - Answers -horizontal compression
f(x)=sin(ax) when a<1
What kind of transformation is this? - Answers -horizontal stretch
f(x)=(-x)^2
What kind of transformation is this? - Answers -reflection over the x-axis
f(x)=-x^2
What kind of transformation is this? - Answers -reflection over the y-axis
f(x)=a(x-h)^2 +k
What is this called? - Answers -vertex form of a quadratic
What is the domain for composition functions when they are sums, differences, or
products? f(g(x)) - Answers -Where f(x) and g(x) overlap
What is the domain for composition functions when it is a quotient? f(g(x)) - Answers -
where f(x) and g(x) overlap EXCEPT where g(x)=0
