Question

5. [20 pts] For the function ?(?) = (4?−8)/(?^2−?−6) answer the following to sketch the graph. Do not use a graphing calculator.

a. [2 pts] Determine the domain of the function, write your answer in interval notation: |
b. [4 pts] Find the x-intercept(s), if any. |
c. [2pts] Find the y-intercept, if any. |
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d. [2 pts] Find the vertical asymptotes, if any. |
e. [2 pts] Find the horizontal asymptote(s) or slant asymptote, if any. |
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f. [4 pts] Determine whether the graph of f(x) crosses the horizontal or slant asymptote, if yes find where. |
g. [4 pts] Sketch the graph of f(x). Label all intercepts, all asymptotes, and any other points used, if any. |

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.

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.

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:

Find the horizontal intercepts, the vertical intercept, the
vertical asymptotes, and the horizontal or slant asymptote of the
function. Use that information to sketch a graph.
g(x) = x-5/3x-1

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)

f(x)=((2x+4)(5x+2))/((7x+8)(7x+6))
1. Find the vertical asymptote(s). If there is more than one
vertical asymptote give a list of the xx-values separated by
commas. If there are no vertical asymptotes, type in none
.
x=
2. If this function has a horizontal asymptote, give its
yy-value. If there is no horizontal asymptote, type in
none
y=
3. Find the xx-intercept(s). If there is more than one
xx-intercept give a list of the xx-intercepts separated by commas
(i.e.: (1,2),(3,4)). If there is...

Find a rational function with x-intercepts –2 and 5, y-intercept
5, and vertical asymptotes x = 3 and x = 6. State the horizontal
asymptote of the graph of the function.

5. (10 pts) Let ?(?) = ?^2−1/ 2?^2+3?+1
a) Simplify the function and find all asymptotes
algebraically.
b) Sketch the graph of ?(?) with the help of a calculator,
indicate the asymptotes, the possible hole, and the x- and
y-intercepts on your graph.

Consider the function ?(?) = log3(3? + 15) − 4. Use algebra to
determine the domain, range, asymptote, ?-intercept, and
?-intercept (if any). [6 pts] Sketch the graph. [4

For the rational function f(x)= (3x^3 - 27x^2 + 60x) / (2x^2 +
2x - 40) find the domain, x-intercepts, y-intercept, and vertical
asymptote/ vertical asymptotes.

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