Question

Describe how each function is a transformation of the original function f(x).

a. -f(3x)

Write a formula for the function that results when the given toolkit function is transformed as described.

a. f(x)=|x| refelcted over the y axis and horizontally compressed by a factor of 1/4.

b. f(x)=√x refelcted over the x axis and horizontally stretched by a factor of 2.

c. f(x)=1/x^2 vertically compressed by a factor of 1/3, then shifted to the left 2 units and down 3 units.

Answer #1

1. Write the new function y=x^3 is reflected with respect to the
x axis, stretched by a factor of 5, shifted to the left 4 units and
shifted down 1 unit.
1a. solve by factoring
Ix^2-x-6I=6
1b. solve using quadratic formula
3x^2+2x=-1
1c. Explain how g(x) is transformed from the graph of y=x^2
The formula is g(x)=5(x+2)^2-5
Vertex coordinates is(-2,-5)

Consider the function f(x) = 4 + x cos x.
Write an equation for :
a) A function g(x) such that the graph of g(x) is the graph of
f(x), shifted 3 units to the right and scaled with factor 1
vertically.
b) A function h(x) such that the graph of h(x) is the graph of
f(x), compressed by a factor 3 horizontally and reflected about the
y-axis.

Write the new function f(x) that satisfies the following
conditions: y =/x/ is reflected with respect to the x-axis,
compressed by a factor of 1/3 , shifted to the left three units,
and up five units.
This is all the information that was given

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

Problem 1: Find a non-zero function f so that f'(x) = 3f(x).
The exponential
function f(x) = e^x has the property that it is its own
derivative.
(d/dx) e^x = e^x
f(x) = e^(3x)
f '(x) = e^(3x) *
(d/dx) 3x
= e^(3x) * 3
= 3e^(3x)
= 3 f(x)
Problem 2: Let f be your function from Problem 1. Show
that if g is another function satisfying g'(x) = 3g(x), then g(x) =
A f(x) for some constant A????

suppose that f'(x)=3x^2+2x+7 and f(1)=11. find the function
f(x)

1. At x = 1, the function g( x ) = 5x ln(x) −
3x
is . . .
Group of answer choices
has a critical point and is concave up
decreasing and concave up
decreasing and concave down
increasing and concave up
increasing and concave down
2. The maximum value of the function f ( x ) = 5xe^−2x
over the domain [ 0 , 2 ] is y = …
Group of answer choices
10/e
0
5/2e
e^2/5...

given function f(x)=-x^3+5x^2-3x+2
A) Determine the intervals where F(x) Is increasing and
decreasing
b) use your answer from a to determine any relative maxima or
minima of the function
c) Find that intervals where f(x) is concave up and concave
down and any points of inflection

For the function , (1)/(3)x^(3)-3x^(2)+8x+11
1)at x=, f(x) attains a local maximum value of
f(x)
2)at x=, f(x) attains a local minimum value of f(x)

Consider the function f(x)= squareroot of (3x)
1) find the linear approximation to the function f at a=4
2) use the linear approximation from part 1 to estimate
squareroot of (12.6)

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