1. At which values of x does the graph of f(x)=cos x intersect the x-axis? Select all that apply. (2 answers)
a. 0***
b. pi/2***
c. pi
d. 3pi/2
e. 2pi
2. Which of the following represents the domain and range of y=tan x?
a. domain: -infinity<x<infinity
range: -infinity<y<infinity, y does not =pi/2+n(pi), where n is an integer
b. domain: -infinity<x<infinity
1. pi/2 and 3pi/2
2. f(x)=cotx
3. domain: -inf<x<inf, x does not equal pi/2+npi, where n is an integer
range: -inf<y<inf
4. f(x)=cotx and f(x)=secx
5. It is true, because the cosine function has a period of 2pi
6. f(x) has no zeros and f(x) has a period of 2pi
7. right pi/4
8. 4pi
9. It has an amplitude of 1/4 and it is a horizontal shift of the parent function pi/3 units left
10. the amplitude and the vertical shift
js took quiz 10/10
Thank you so much random junior I got 100%
Appreciate it random junior
please ignore the last question I meant to delete it:)
Thank you Steve. Can you explain this question to me please?
cosx = 0 for all odd multiples of pi/2
a is wrong -- cos 0 = 1
To find the values of x where the graph of f(x) = cos x intersects the x-axis, we need to find the x-values where f(x) equals zero. In other words, we need to solve the equation cos x = 0.
1. The equation cos x = 0 has solutions at x = pi/2 and x = 3pi/2. These values can be obtained by using the unit circle or a calculator.
Therefore, the values of x at which the graph of f(x) = cos x intersects the x-axis are:
a. 0 (since cos 0 = 1)
b. pi/2 (since cos(pi/2) = 0)
Now let's move on to the second question.
To determine the domain and range of y = tan x, we first need to understand the properties of the tangent function.
The tangent function, tan x, is defined for all real numbers except for values that make the cosine function equal to zero. Since the cosine function equals zero when x = (n + 1/2)pi, where n is an integer, we need to exclude these values from the domain.
Similarly, the range of the tangent function is all real numbers except y = pi/2 + n(pi), where n is an integer.
2. The correct answer is a.
The domain of y = tan x is -infinity < x < infinity, excluding x = (n + 1/2)pi, where n is an integer.
The range of y = tan x is -infinity < y < infinity, excluding y = pi/2 + n(pi), where n is an integer.
I hope this explanation helps you understand how to find the values of x that satisfy certain conditions and determine the domain and range of a function.
huh? I thought I did. cos(x) oscillates between 1 and -1, with a period of 2pi.
cos(0) = 1
cos(pi/2) = 0
cos(pi) = -1
cos 3pi/2 = 0
cos 2pi = 1
and it repeats all over again. Note that cosx is zero at all odd multiples of pi/2
So, you should have picked (b) and (d)
If this still makes no sense, you really really need to review the trig functions!