Question

. Find a cubic function f(x) with roots x = 4, x = 1, x = −2 and f(1) = 16.

3. Sketch the graph of f(x) = (x − 2)/x^2−3x−4 showing zeros, intercepts, and asymptotes.

4. Assume that world population(in billions of people) in t years since 2016 is given by y = 7.7e^0.01t . When will the population reach 9 billion?

5. Solve for x: log3 (x + 2) + log3 (x − 4) = 3.

6. Show that sec x = 2 sin x / sin(2x)

7. Graph one period of y = −3 cos (x/3 − π/ 2) . What are the period, amplitude and phase shift?

8. A triangle has sides a = 2, b = 5, and c = 6. Solve the triangle.

9. Graph (x − 2)^2 / 9 − (y + 1)^2 /16 = 1, labeling the center, vertices and foci.

10. Expand (x − 2y)^5 .

11. Triangle ABC has measures of b= 8, c = 12, and A = 50 degrees. Solve the triangle.

Answer #1

For the function f(x) = ? 3−1 ? 2−9 , find any slant asymptotes
and sketch the graph by finding any vertical asymptotes, horizontal
asymptotes, x intercepts, y intercept.

Find the hyperbolic equation
8) Foci F(±4, 0) and asymptotes y = ± [x√(14) / √(2)]
9) Foci F(0, ±√(19)) and asymptotes y = ± [2x√(3) / √(7)]
10) Foci F(±11, 0) and asymptotes y = ± [2x√(10) / 9]

Graph f(x)=
x3-x2-16x+16/2x2-18
List and mark the vertical and horizontal asymptotes, oblique
asymptotes, zeros, and y- intercepts on the graph.

Sketch the graph of the function f(x) = x − 4 / x + 4 using the
guidelines below, a. Determine the domain of f.
b. Find the x and y intercepts.
c. Find all horizontal and vertical asymptotes.
d. Determine the intervals of increasing/decreasing.
e. Determine the concavity of f.

Let f(x) be a function that is continuous for all real numbers
and assume all the intercepts of f, f' , and f” are given below.
Use the information to a) summarize any and all asymptotes,
critical numbers, local mins/maxs, PIPs, and inflection points, b)
then graph y = f(x) labeling all the pertinent features from part
a. f(0) = 1, f(2) = 0, f(4) = 1 f ' (2) = 0, f' (x) < 0 on (−∞,
2), and...

Analyze and plot the graph of f(x)= x^4/2 - 2x^3/3. for this,
find;
1) domain of f:
2)Vertical asymptotes:
3) Horizontal asymptotes:
4) Intersection in y:
5) intersection in x:
6) Critical numbers
7) intervals where f is increasing:
8) Intervals where f is decreasing:
9) Relatives extremes
Relatives minimums:
Relatives maximums:
10) Inflection points:
11) Intervals where f is concave upwards:
12) intervals where f is concave down:
13) plot the graph of f on the plane:

Lef f(x) = -(x+4)(x-1)^3(x-3)^2 = -x^6 + 5x^5 + 6x^4 - 74x^3 +
151x^2 - 123x + 36
1.)Determine the end behavior
2.) Find the real zeros of f(x) & state the multiplicity of
each zero. Determine the manner in which the graph of f(x) crosses
or touches the x-axis at each zero.
3.) Find the x-intercepts and the y-intercept
4.) Draw the graph of f(x)
Please show work for answers- thanks :)

Find traits and sketch the graph the equation
for a function g ( x ) that shifts the function f ( x ) = x + 4 x 2
− 16 two units right. Label and scale your
axes.
Domain:
x – Intercepts:
y – Intercept:
Vertical Asymptotes:
Holes:
End Behavior:
Range:

Let ?(?)=2?3−9x^2+3?+4.
List all possible rational roots of ?g, according to the
Rational Zeros Theorem.
You must list positive and negative roots separately (there is no
±± in WeBWorK).
Separate your list with commas.
Factor ? completely:
?(?)=____
The x-intercepts of the graph of ?=?(?) are:
Note: Use commas to separate your answers.
?=___
The y-intercept of the graph of ?=?(?) is:
?=____
Select the correct graph of ?=?(?): ? Graph A Graph
B Graph C Graph D Graph E Graph...

Find the vertical asymptotes, horizontal asymptote, and x and y
intercepts of the following function and sketch a graph
f(x) = (x^2 − 4) / (x^2 − 2x − 15)

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