Question

Q1: Sketch the graph of polynomial ?(?)=?3−?. Label the coordinates of the x- and y-intercepts, stationary point, and inflection point.

Answer #1

Clearly sketch the graph of y=x- 2 /(x+3)^2 and label in your
graph everything (intercepts, asymptotes, extrema, inflection
points)

Sketch the following function, y = 5x3 + 7x2 + 2x
Label the coordinates for the maximum, minimum and inflection
points. Demonstrate the process to be followed in sketching this
curve by hand.

Question 1a Consider the polynomial function P(x) = x3+x2−20x.
Sketch a graph of y = P(x) by: determining the zeros of P(x),
identifying the y-intercept of y = P(x), using test points to
examine the sign of P(x) to either side of each zero and deducing
the end behaviour of the polynomial.
b Consider the quadratic function f(x) = 2x2 + 8x−1. (a) Express
f(x) in standard form. (b) Determine the vertex of f(x). (c)
Determine the x- and y-intercepts...

Curve Sketching Practice
Use the information to the side to sketch the graph of
f.
Label any asymptotes, local extrema, and inflection
points.
f is a polynomial function
x
—1
—6
3
—2
6
5
f is a polynomial function
x
1
—4
4
0
7
4

Find the coordinates of the x-intercepts of the graph
of the equation. (If an answer does not exist, enter DNE.)
y = x2 ? 16
(x,y) = (______) smaller value
(x,y) = (______) larger value

1. Graph of the function and label any intercepts and
asymptotes.
R(x)= x+5/x(x-3)

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

given the polynomial function f(x)=x^2(x-3)(x+1)
find x and y intercepts of f(x) and determine whether the
graph of f crosses or touches the x-axis at each x-intercept.

Given the polynomial function f(x)=(x-a)(x-b)^2, and
a<0<b, find the following:
A). Sketch the graph
B). find the x and the y intercepts
C). find the solution to f(x)<0
D). find the solution to f(x) is greater than or equal to 0

Given that a polynomial function g has g(1)=-96, and has
x-intercepts at x = -3 (multiplicity 3), x=-1 (m.1), and 2 (m. 2),
sketch the graph of the function, then write a equation for g(x)
(can leave function in factored form) and describe its end
behavior.

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