ANSWER TO QUESTION 1
We have the function
.
The domain of this function refers to all -values for which is defined.
This is a rational function that is undefined whenever the denominator is equal to zero. As a result of this we need to exclude the x-values that will make the function undefined.
We can find these values by equating the the denominator to zero.
Also this rational function is undefined whenever the expression under the radical sign in the numerator is less than zero.
We must therefore restrict the expression under the square root sign in the numerator to be greater or equal to zero. Thus
Because of this last restriction, is eliminated from the restrictions.
Therefore the domain of is
,
The correct answer is C
ANSWER TO QUESTION 2
We have the function
which is a maximum function written in the vertex form.
It is a maximum function because when we compare to the general vertex form,
The vertex of the graph is .
The x-value of the vertex is
For , the graph is increasing and for the graph will be decreasing.
The correct answer is C
ANSWER TO QUESTION 3
and
The correct answer is C
ANSWER TO QUESTION 4
We have
The composition of the two functions
is given by;
This implies that;
The correct answer is B.
ANSWER TO QUESTION 5.
Given
.
Then
and
So that;
Which will give;
.
The correct answer is A
ANSWER TO QUESTION 6
The dimension of the smallest region are
km
and
If the length and width are increasing at the rate of 3km\sec, then after seconds, the dimensions will be,
km
and
km
This means the area after seconds is given by;
.
If the area is at least 4 times its original size, then we can write the inequality;
.
We expand to obtain;
We simplify to obtain,
We split factor to get;
This implies that;
or
Since we are dealing with time, we discard the negative value. Hence it will take
The correct answer is D.
ANSWER TO QUESTION 8
The correct answer is C.
This is how the following transformations affect the graph of
If , the graph opens down.
If , the graph opens up.
If , the graph graph shifts to the right b units.
If , the graph graph shifts to the left b units.
If , the graph graph shifts down c units.
If ,the graph graph shifts up c units.
Therefore for , the graph of moves to the right 14 units and moves down 9 units.
ANSWER TO QUESTION 9
The graph of
has y-intercept which is
and
has x-intercept which is
In order to transform the graph of in to , we need to shift the x-intercept of the graph of f 14 units to the left.
The correct answer is C
ANSWER TO QUESTION 10
The function;
.
This is a polynomial with a degree of 5 and the leading coefficient is .
The correct answer is C
ANSWER TO QUESTION 11
We have
We add and subtract half the coefficient of .
The first three term is a perfect square.
The correct answer is A.
ANSWER TO QUESTION 12
We want to solve;
To find the zeros of this function, we equate it to zero.
We factor to obtain;
We now split the middle term of the quadratic factor to get,
The correct answer is C.
See Attachment for the rest of the solutions
15. Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24
The constant term of () is -24
The leading coefficient is 1.
We have to only consider the factors of the constant (leading coefficient = 1)
The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±241) Find the domain
of the given function.
f(x) = square root of quantity x plus three divided by quantity x plus eight
times quantity x minus two.
using a graphical tool see the attachment
the answer is C) x ≥ -3, x ≠ 2
2. Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 2 - (x - 7)2
using a graphical tool
see the attachment
the answer is C) Increasing: x < 7; decreasing: x > 7
3. Perform the
requested operation or operations.
f(x) = 4x + 7, g(x) = 3x2
Find (f + g)(x).
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 4x + 7 + 3x^2
(f + g)(x) = 3x^2 + 4x + 7
The answer is C) 4x + 7 + 3x2
4. Perform the requested operation or operations.
f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).
f(x)=(x-5)/8 g(x)=8x+5
g(f(x))=8((x-5)/8)+5=x-5+5=x
the answer is B) g(f(x)) = x5. Find f(x) and
g(x) so that the function can be described as y = f(g(x)).
y = nine divided by square root of quantity five x plus five.
y=f(g(x))=9/((5x+5) ^1/2)
let do
g(x)=5x+5...........so
f(x)= 9/( x^1/2)
the answer is A) f(x) = nine divided by square root of x. , g(x) = 5x + 56. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Original size- >4km*4km=16 km2
4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km
Therefore
3km----------------------------- 1 sec
(8km-4km)---------------------x
X=4/3=1.33 sec
The answer is D) 1.33 sec7. Find the inverse of the function.
f(x) = the cube root of quantity x divided by seven. - 9
to solve
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
f(x)=((x/7)-9) ^(1/3)
replace f(x) with y
y=((x/7)-9) ^(1/3)
switch x and y
x=((y/7)-9) ^(1/3)
solve for y
x^3=((y/7)-9)
x^3+9=y/7
y=7(x^3+9)
the answer is C) f-1(x) = 7(x3 + 9)8. Describe how
the graph of y= x2 can be transformed to the graph of the given equation.
y = (x - 14)2 – 9
9. Describe how
to transform the graph of f into the graph of g.
f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root
of quantity x plus five. '
f(x)=(x-9) ^1/2 g(x)=(x+5) ^1/2
using a graphical tool see the attachment10. If the
following is a polynomial function, then state its degree and leading
coefficient. If it is not, then state this fact.
f(x) = -16x5 - 7x4 – 6
11. Write the
quadratic function in vertex form.
y = x2 + 4x + 7
Complete the square on the right side of the equation
Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=7
Consider the vertex form of a parabola.
a(x+d)2+e
Find the value of dd using the formula d=b/2a
d=4/(2*1)=2
Find the value of e using the formula e=c−b2/4a
e=7−4=3
Substitute the values of a, d, and e into the vertex form a(x+d)2+e
(x+2)2+3
The answer is A) y = (x + 2)2+ 312. Find the zeros of the function.
f(x) = 3x3 - 12x2 - 15x
using a graphical tool (see the attachment)x1=-1
x2=0
x3=5
The answer is C) 0, -1, and 513. Find a cubic
function with the given zeros.
7, -3, 2
X1=7
X2=-3
X3=2
f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42
the answer is C) f(x) = x3 - 6x2 - 13x + 4214. Find the
remainder when f(x) is divided by (x - k).
f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3
f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946
The answer is the B) 94615. Use the
Rational Zeros Theorem to write a list of all potential rational zeros.
f(x) = x3 - 10x2 + 4x - 24
The constant term of
15. Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24
The constant term of () is -24
The leading coefficient is 1.
We have to only consider the factors of the constant (leading coefficient = 1)
The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24The answer is in the image
For every 8 cars there are 7 trucks
Therefore,
Cars:Truck=8:7
Answer is B)8:7
The answer is in the image
F=ma
where F=force
m=mass
a=acceleration
Here,
F=4300
a=3.3m/s2
m=F/a
=4300/3.3
=1303.03kg
Salesperson will make 6% of 1800
=(6/100)*1800
=108
Salesperson will make $108 in $1800 sales
The answer is in the image
It will provide an instant answer!