Question

Q 1) Consider the following functions.

f(x) = 2/x, g(x) = 3x + 12

Find (f ∘ g)(x).

Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)

Find (g ∘ f)(x).

Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)

Find (f ∘ f)(x).

Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)

Find (g ∘ g)(x).

Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)

Q 2) Find the exponential function

f(x) = a^{x} whose graph is given.

{ Point on the graph (-1, 1/10) }

f(x) | = |

Q 3 )Find the exponential function

f(x) = a^{x} whose graph is given.

{ Point on the graph (2, 1/25) }

f(x) | = |

Q 4)

The sine curve y = a sin(k(x − b)) has amplitude [ ] , period [ ] , and horizontal shift [ ] . The sine curve y = 3 sin (7(x − π/4) has amplitude [ ] , period [ ], and horizontal shift [ ].

Answer #1

Find each of the following functions. f(x) = 4 − 4x, g(x) =
cos(x)
(a) f ∘ g and State the domain of the function. (Enter your
answer using interval notation.)
(b) g ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(c) f ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(d) g ∘ g and State the domain of the function. (Enter your
answer using...

1a.
Find the domain and range of the function. (Enter your answer
using interval notation.)
f(x) = −|x + 8|
domain=
range=
1b.
Consider the following function. Find the composite
functions
f ∘ g
and
g ∘ f.
Find the domain of each composite function. (Enter your domains
using interval notation.)
f(x) =
x − 3
g(x) = x2
(f ∘ g)(x)=
domain =
(g ∘ f)(x) =
domain
are the two functions equal?
y
n
1c.
Convert the radian...

1. Consider the function.
f(x) = 6x − 9
(a) Find the inverse function of f.
(b) Graph f and f −1 on the same
set of coordinate axes.
(c) Describe the relationship between the graphs. The graphs of
f and f −1 are reflections of each
other across the line y =
(d) State the domain and range of f and f
−1. (Enter your answers using interval notation.)
2.
Consider the function.
f(x) = x+3/x
(a) Find the...

question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

Consider the function below. (If an answer does not exist, enter
DNE.)
f(x) = 1/2x^(4) − 4x^(2) + 3
(a)
Find the interval of increase. (Enter your answer using interval
notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b)
Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c)
Find the inflection points.
(x, y) = (smaller x-value)
(x, y) =...

Consider the function on the interval (0, 2π).
f(x) =
sin(x)/
2 + (cos(x))2
(a) Find the open intervals on which the function is increasing
or decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) Apply the First Derivative Test to identify the relative
extrema.
relative maximum
(x, y) =
relative minimum
(x, y) =

a.)Consider the function f (x) = 3x/ x^2 +1
i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the
same for f (2x) and 2f (x).
ii) Sketch y = f (x) on the interval [−2, 2].
iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each
case, if a solution does not exist, explain.
iv) What is the domain of f (x)?
b.)Let f (x) = √x −1 and g (x) =...

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

Consider the function below. (If an answer does not exist, enter
DNE.)
g(x) = 250 +
8x3 +
x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection points.
(x, y)=(smaller x-value)
(x, y)=(larger x-value)
Find the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 6 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 41 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 52 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago