POLYNOMIAL FUNCTIONS
Describe the end behavior of f(x)=3x^4 using the leading coefficient and degree, and state the domain and range.
As x→−∞, f(x)→∞ and as x→∞, and f(x)→∞;D=(−∞,∞), R=[0,∞)
Determine the consecutive integer values of x between which each real zero of f(x)=x^2+3x−1 is located by using a table. Then sketch the graph on a separate sheet of paper.
zeros between x=−4 and x=−3, and x=0 and x=1
Determine whether a^3−11 is a polynomial. If it is a polynomial, state the degree of the polynomial.
yes, 3
Simplify the expression. Write the expression in standard form.
15y3+6y2+3y/3y
5y^2+2y+1
State the degree and leading coefficient of the polynomial in one variable. If it is not a polynomial in one variable, explain why.
(2x−1)(4x^2+3)
Degree= 3
Coefficient: 8
n+8
Degree:
Leading Coefficient:
1 and 1
Determine the consecutive integer values of x between which each real zero of f(x)=−x^3+2x^2−4 is located by using a table. Then sketch the graph on a separate sheet of paper.
zero between x=−2 and x=−1
Determine whether 5np/n^2−2g/h is a polynomial. If it is a polynomial, state the degree of the polynomial.
no
Simplify the expression. Write the expression in standard form, and order the terms alphabetically.
(6j^2k−9jk^2)÷(3jk)
2j−3k
Add or subtract. Write the expression in standard form.
(g+5)+(2g+7)
3g+12
Describe the end behavior of f(x)=−2x^3 using the leading coefficient and degree, and state the domain and range.
As x→−∞, f(x)→∞ and as x→∞, and f(x)→−∞;D=(−∞,∞), R=(−∞,∞)
Use a table to graph f(x)=−2x^3+12x^2−8x on a separate sheet of paper. Then estimate the x-coordinates at which relative maxima and relative minima occur.
The relative minima occur between x=0 and x=1
the relative maxima occur near x=4
Determine whether (square root) m−7 is a polynomial. If it is a polynomial, state the degree of the polynomial.
no
Simplify by using long division. Write the expression in standard form.
(6y^2+y−2)(2y−1)−1
3y+2
Subtract. (2/3x−3)−(1/6x−6)
x/2+3
Describe the end behavior of f(x)=−1/2x^5 using the leading coefficient and degree, and state the domain and range.
As x→−∞, f(x)→∞ and as x→∞, and f(x)→−∞;D=(−∞,∞), R=(−∞,∞)
Use a table to graph f(x)=x^4+2x−1 on a separate sheet of paper. Then estimate the x-coordinates at which relative maxima and relative minima occur.
The relative maxima occur near x= No maxima
the relative minima occur near x= -1
Add or subtract. Write the expression in standard form.
(6a2+5a+10)−(4a2+6a+12)
2a^2−a−2
Simplify by using long division. Write the expression in standard form.
(4g^2−9)÷(2g+3)
2g−3
Simplify using synthetic division. Write the expression in standard form.
y^3+6/y+2
y^2−2y+4−/2y+2
Describe the end behavior of f(x)=3/4x^6 using the leading coefficient and degree, and state the domain and range.
As x→−∞, f(x)→∞ and as x→∞, and f(x)→∞;D=(−∞,∞), R=[0,∞)
Determine whether 2x^2−3x+5 is a polynomial. If it is a polynomial, state the degree of the polynomial.
yes, 2
Add or subtract. Write the expression in standard form.
(7b2+6b−7)−(4b2−2)
3b^2+6b−5
Simplify using synthetic division. Write the expression in standard form.
(3v^2−7v−10)(v−4)−1
3v+5+10/v−4
Simplify. Write the expression in standard form.
(m^2+m−6)÷(m+4)
m−3+6/m+4