For each function, indicate the amplitude, frequency, period, phase shift, horizontal and vertical translations, and
equation of the midline. graph the function together with a graph of the sine function ) = cos(x) on the same
axes. graph at least one full period of each function. no calculators are allowed.
a. ) = cos(3x)
b. ) = cos (x − / 4 )
c. ) = 3 cos (x / 4)
d. ) = 3 cos(2x) − 4
e. ) = 4 cos / 4 − 2x) (hint: first, rewrite the function in the form ) = − ℎ

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation:

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.