Question

Sketch the graph of a function f(x) that satisfies all of the conditions listed below. Be sure to clearly label the axes.

f(x) is continuous and differentiable on its entire domain, which is (−5,∞)

limx→-5^+ f(x)=∞

- limx→∞f(x)=0limx→∞f(x)=0
- f(−2)=−4,f′(−2)=0f(−2)=−4,f′(−2)=0
- f′′(x)>0f″(x)>0 for −5<x<1−5<x<1
- f′′(x)<0f″(x)<0 for x>1x>1

Answer #1

sketch the graph of one and only one function that satisfies all
the conditions listed below:
a. f(-x) = -f(x)
b. lim as x approaches 4- f(x)= infinity
c.lim as x approaches 4+ f(x)=-infinity
d. Limit as x approaches infinity f(x)=2
e. the second derivative of f(x) >0 on the interval (0,4)

7. (a) Sketch a graph of a function f(x) that satisfies all of
the following conditions.
i. f(2) = 3 and f(1) = −1
ii. lim x→−4 f(x) = −∞
iii. limx→∞ f(x) = 1
iv. lim x→−∞ f(x) = −2
v. lim x→−1+ f(x) = ∞
vi. lim x→−1− f(x) = −∞
vii. f 0 (x) > 0 on (−4, −3.5) ∪ (−2.5, −1.5) ∪ (1, 2) ∪ (2,
∞)
viii. f 0 (x) < 0 on (−∞, −4)...

Sketch a graph of a function that satisfies the following
conditions. Then take a picture and upload your graph.
f is continuous and even
f(2) = -1
f'(x) = 2x if 0 < x < 2
f'(x) = -2/3 if 2 < x < 5
f'(x) = 0 if x > 5

Sketch the graph of a function that is
continuous on (−∞,∞) and satisfies the following sets of
conditions.
f″(x) > 0 on (−∞,−2); f″(−2) = 0; f′(−1) = f′(1) = 0; f″(2) =
0; f′(3) = 0; f″(x) > 0 on ( 4, ∞)

Sketch a possible graph of a function that satisfies the
conditions:
? (0 ) = 2, ?′(?)
> 0 ?? (−∞,4), ?′(?)
< 0 ?? (4,∞), f is concave down everywhere.

Sketch a continuous graph that satisfies each set of
conditions.
d) f"(x)=1 when x>-2, f"(x)=-1 when x<-2, f(-2)=-4

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:

Sketch the graph of a function that satisfies the given criteria.
f(1) = 0, f^ prime (-1)=f^ prime (2)=f^ prime (10)=0 lim x
infty f(x)=1 lim x 6 f(x)=- infty f^ prime (x)<0 ort(-
infty,-1),(2,7),(10, infty) f^ prime (x)>0 on(-1,2),(7,10) f^
prime prime (x)>0 on(- infty,1),(13, infty) f^ prime prime
(x)<0 on (1,7),(7,13)

Sketch the graph of a function f that is continuous on (−∞,∞)
and has all of the following properties:
(a) f0(1) is undeﬁned
(b) f0(x) > 0 on (−∞,−1)
(c) f is decreasing on (−1,∞).
Sketch a function f on some interval where f has one inﬂection
point, but no local extrema.

For the following exercises, draw a graph that satisfies the
given specifications for the domain x=[−3,3]. The function does not
have to be continuous or differentiable.
216.
f(x)>0,f′(x)>0 over x>1,−3<x<0,f′(x)=0 over
0<x<1
217.
f′(x)>0 over x>2,−3<x<−1,f′(x)<0 over
−1<x<2,f″(x)<0 for all x
218.
f″(x)<0 over
−1<x<1,f″(x)>0,−3<x<−1,1<x<3, local maximum at
x=0, local minima at x=±2
219.
There is a local maximum at x=2, local minimum at x=1, and the
graph is neither concave up nor concave down.

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