MATH 101 FINAL REVIEW EXAM
QUESTIONS AND ANSWERS (VERIFIED
AND UPDATED)
Definition of a function - ANS each input has exactly one output
How to tell if a relation is a function - ANS -Passes VLT
-x values do not repeat in ordered pairs
Domain - ANS x values. Written in interval notation
Range - ANS y values, written in interval notation
How to find the y-intercept - ANS Let x = 0 and solve for y. (0, y)
how to find the x intercept(s) of a rational function - ANS factor the top, set the numerator =
0 and solve.
increasing interval - ANS The interval of X values where the y-values are increasing over the
interval. ALWAYS USE PARENTHESIS
decreasing interval - ANS The interval of X values where the y-values are decreasing over the
interval. ALWAYS USE PARENTHESIS
@2026/2027 ALLRIGHTS RESERVED.
, f(x)=x^2, Quadratic Function (shape & parent points) - ANS Parabola, Parent points: (-2, 4)(-1,
1)(0,0)(1, 1)(2, 4)
square root function (equation, shape, and parent points) - ANS f(x)=√x, Parent
points:(0,0)(1, 1)(4, 2)(9, 3)
absolute value function (equation, shape, and parent points) - ANS f(x)=|x|, Parent points: (-
2, 2)(-1,1)(0,0)(1,1)(2,1)
Asymptote for Exponential Functions - ANS HORIZONTAL, y=k
Asymptote for Logarithm Functions - ANS VERTICAL, x=h
(f o g)(x)= - ANS Means f of g of x. Put g into f, f(g(x))
NOT MULTIPLICATION
In, y=af(b(x-h))+ k, what does A do to the graph? - ANS vertical stretch or compression. To
apply this to your graph, multiply your Y values by A.
In, y=af(b(x-h))+ k, what does B do to the graph? - ANS horizontal stretch or compression. To
apply this to your graph, multiply your X values by 1/B
In, y=af(b(x-h))+ k, what does H do to the graph? - ANS Shifts the graph left or right. To apply
this to your graph, add or subtract your X values by h
In, y=af(b(x-h))+ k, what does K do to the graph? - ANS Shifts the graph up or down. To apply
this to your graph, add or subtract your X values by K
Average rate of change [a, b] (formula) - ANS (f(b)-f(a))/(b-a)
@2026/2027 ALLRIGHTS RESERVED.
QUESTIONS AND ANSWERS (VERIFIED
AND UPDATED)
Definition of a function - ANS each input has exactly one output
How to tell if a relation is a function - ANS -Passes VLT
-x values do not repeat in ordered pairs
Domain - ANS x values. Written in interval notation
Range - ANS y values, written in interval notation
How to find the y-intercept - ANS Let x = 0 and solve for y. (0, y)
how to find the x intercept(s) of a rational function - ANS factor the top, set the numerator =
0 and solve.
increasing interval - ANS The interval of X values where the y-values are increasing over the
interval. ALWAYS USE PARENTHESIS
decreasing interval - ANS The interval of X values where the y-values are decreasing over the
interval. ALWAYS USE PARENTHESIS
@2026/2027 ALLRIGHTS RESERVED.
, f(x)=x^2, Quadratic Function (shape & parent points) - ANS Parabola, Parent points: (-2, 4)(-1,
1)(0,0)(1, 1)(2, 4)
square root function (equation, shape, and parent points) - ANS f(x)=√x, Parent
points:(0,0)(1, 1)(4, 2)(9, 3)
absolute value function (equation, shape, and parent points) - ANS f(x)=|x|, Parent points: (-
2, 2)(-1,1)(0,0)(1,1)(2,1)
Asymptote for Exponential Functions - ANS HORIZONTAL, y=k
Asymptote for Logarithm Functions - ANS VERTICAL, x=h
(f o g)(x)= - ANS Means f of g of x. Put g into f, f(g(x))
NOT MULTIPLICATION
In, y=af(b(x-h))+ k, what does A do to the graph? - ANS vertical stretch or compression. To
apply this to your graph, multiply your Y values by A.
In, y=af(b(x-h))+ k, what does B do to the graph? - ANS horizontal stretch or compression. To
apply this to your graph, multiply your X values by 1/B
In, y=af(b(x-h))+ k, what does H do to the graph? - ANS Shifts the graph left or right. To apply
this to your graph, add or subtract your X values by h
In, y=af(b(x-h))+ k, what does K do to the graph? - ANS Shifts the graph up or down. To apply
this to your graph, add or subtract your X values by K
Average rate of change [a, b] (formula) - ANS (f(b)-f(a))/(b-a)
@2026/2027 ALLRIGHTS RESERVED.
