MATH 1222 INTRODUCTION
ALGEBRA MODULE FINAL
ASSESSMENT 2026 STUDY GUIDE
COMPREHENSIVE QUESTIONS
ANSWERS VERIFIED A+
◉ Why are the quadratic and cubic functions power functions?
Answer: Because they have whole number powers
◉ Why are the reciprocal functions power functions?
Answer: Because they have negative whole powers. f(x) = 1/x is
equivalent to x^-1, while 1/x^2 is equivalent to x^-2.
◉ Why are the square and cube root functions power functions?
Answer: Because they have fractional powers. Sqrt(x) = x^1/2 and
cbrt(x) = x^1/3
◉ How do you determine the long-run behavior of a
function/polynomial?
Answer: For any polynomial, the long run behavior of the polynomial
will match the long run behavior of the leading term.
◉ What is the long-run behavior of a polynomial with an odd degree?
Answer: x→oo, f(x) →-oo
x →-oo, f(x) →oo
,◉ What is the vertical intercept and how do you find it?
Answer: The vertical intercept is the y-intercept, which means it is found
when the values of x = 0.
◉ What is the horizontal intercept and how do you find it?
Answer: The horizontal intercept is the x-intercept. Often, there are
multiple of these. They can also be called zeros. They are found by
setting the y-value to zero, which can be found through synthetic
division, factoring, completing the square, using the quadratic fraction,
or other methods.
◉ How does the degree of a polynomial relate to the horizontal
intercepts/how to find the maximum number of real zeros?
Answer: A polynomial with a degree of n(any number) will have at most
n horizontal intercepts. Whatever the degree is, that is the maximum of
x-intercepts it has. Odd degree polynomials always have at least one x-
intercept.
◉ How can you find the maximum number of turns without drawing a
graph?
Answer: The degree of the polynomial - 1 = the amount of turning
points
◉ What is the long-run behavior of an even polynomial?
Answer: As x →oo, f(x) →oo
,As x →-oo, f(x) →oo
◉ What is the long-run behavior of a negative, even polynomial?
Answer: As x → oo, f(x) →-oo
As x →-oo, f(x) →-oo
◉ What is the long-run behavior of an odd polynomial?
Answer: As x →oo, f(x) → -oo
As x →-oo, f(x) →oo
◉ What is the long-run behavior of a negative, odd polynomial?
Answer: As x →oo, f(x) →-oo
As x → -oo, f(x) → oo
◉ How do you identify the leading term, the degree, and the leading
coefficient of a polynomial?
Answer: A leading term is the term with the highest exponent. The
degree is the highest exponent. The leading coefficient is the number in
front of the leading term.
◉ What exponent do normal numbers without variables have?
Answer: Their degree, or exponent, is zero.
◉ How do you find the least possible degree?
, Answer: Count the number of spots where the graph could have
been/intersect the x-axis.
◉ What is a vertex?
Answer: The part in the graph where the graph changes direction.
◉ When is a vertex a minimum and when is a vertex a maximum?
Answer: A Vertex is a Maximum if the graph opens down, meaning the
highest point on the parabola is when it arches high (a must be greater
than 0). A vertex is a minimum if the graph opens up, meaning the
lowest point is when it droops down before ascending back upward (a
must be less than 0).
◉ How can you tell if the polynomial's vertex is a minimum or a
maximum is not in vertex form(a(x - h)^2 + k)?
Answer: If given ordered pairs, then check the y-values. If the y-values
are less than one, the vertex is a minimum. if the y-values are greater
than one, then the vertex is a maximum.
◉ What are the forms a polynomial can take?
Answer: 1. Standard form: f(x) = ax^2 + bx + c
2. Transformation/vertex form: f(x) = a(x - h)^2 + k
3. Vertex: (h, k).
◉ How do you find the vertex of a quadratic if you are given a
polynomial in standard form?
ALGEBRA MODULE FINAL
ASSESSMENT 2026 STUDY GUIDE
COMPREHENSIVE QUESTIONS
ANSWERS VERIFIED A+
◉ Why are the quadratic and cubic functions power functions?
Answer: Because they have whole number powers
◉ Why are the reciprocal functions power functions?
Answer: Because they have negative whole powers. f(x) = 1/x is
equivalent to x^-1, while 1/x^2 is equivalent to x^-2.
◉ Why are the square and cube root functions power functions?
Answer: Because they have fractional powers. Sqrt(x) = x^1/2 and
cbrt(x) = x^1/3
◉ How do you determine the long-run behavior of a
function/polynomial?
Answer: For any polynomial, the long run behavior of the polynomial
will match the long run behavior of the leading term.
◉ What is the long-run behavior of a polynomial with an odd degree?
Answer: x→oo, f(x) →-oo
x →-oo, f(x) →oo
,◉ What is the vertical intercept and how do you find it?
Answer: The vertical intercept is the y-intercept, which means it is found
when the values of x = 0.
◉ What is the horizontal intercept and how do you find it?
Answer: The horizontal intercept is the x-intercept. Often, there are
multiple of these. They can also be called zeros. They are found by
setting the y-value to zero, which can be found through synthetic
division, factoring, completing the square, using the quadratic fraction,
or other methods.
◉ How does the degree of a polynomial relate to the horizontal
intercepts/how to find the maximum number of real zeros?
Answer: A polynomial with a degree of n(any number) will have at most
n horizontal intercepts. Whatever the degree is, that is the maximum of
x-intercepts it has. Odd degree polynomials always have at least one x-
intercept.
◉ How can you find the maximum number of turns without drawing a
graph?
Answer: The degree of the polynomial - 1 = the amount of turning
points
◉ What is the long-run behavior of an even polynomial?
Answer: As x →oo, f(x) →oo
,As x →-oo, f(x) →oo
◉ What is the long-run behavior of a negative, even polynomial?
Answer: As x → oo, f(x) →-oo
As x →-oo, f(x) →-oo
◉ What is the long-run behavior of an odd polynomial?
Answer: As x →oo, f(x) → -oo
As x →-oo, f(x) →oo
◉ What is the long-run behavior of a negative, odd polynomial?
Answer: As x →oo, f(x) →-oo
As x → -oo, f(x) → oo
◉ How do you identify the leading term, the degree, and the leading
coefficient of a polynomial?
Answer: A leading term is the term with the highest exponent. The
degree is the highest exponent. The leading coefficient is the number in
front of the leading term.
◉ What exponent do normal numbers without variables have?
Answer: Their degree, or exponent, is zero.
◉ How do you find the least possible degree?
, Answer: Count the number of spots where the graph could have
been/intersect the x-axis.
◉ What is a vertex?
Answer: The part in the graph where the graph changes direction.
◉ When is a vertex a minimum and when is a vertex a maximum?
Answer: A Vertex is a Maximum if the graph opens down, meaning the
highest point on the parabola is when it arches high (a must be greater
than 0). A vertex is a minimum if the graph opens up, meaning the
lowest point is when it droops down before ascending back upward (a
must be less than 0).
◉ How can you tell if the polynomial's vertex is a minimum or a
maximum is not in vertex form(a(x - h)^2 + k)?
Answer: If given ordered pairs, then check the y-values. If the y-values
are less than one, the vertex is a minimum. if the y-values are greater
than one, then the vertex is a maximum.
◉ What are the forms a polynomial can take?
Answer: 1. Standard form: f(x) = ax^2 + bx + c
2. Transformation/vertex form: f(x) = a(x - h)^2 + k
3. Vertex: (h, k).
◉ How do you find the vertex of a quadratic if you are given a
polynomial in standard form?
