Step-by-step explanation:
cot x + 2 tan x + tan³ x
Write in terms of sine and cosine:
(cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)
Find the common denominator:
(cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))
Add:
(cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)
Factor:
(sin² x + cos² x)² / (sin x cos³ x)
Pythagorean identity:
1 / (sin x cos³ x)
Multiply top and bottom by cos x:
cos x / (sin x cos⁴ x)
Simplify:
cot x sec⁴ x
Yes, because each input value corresponds to exactly one output value.Yes, because the outputs increase as the inputs increase.No, because the graph is not continuous.No, because the curve indicates that the rate of change is not constant.
Yes you can combine the 7s and the 5s to get 12s then add the plus 8
Y=8,4,2,-2 linear and in that order
Answer:
- Parent Function:

- Horizontal shift: right 3 units
- Vertical shift: up 3 units
- Reflection about the x-axis: none
- Vertical strech: streched
Step-by-step explanation:
assume that
is
and
is

The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.

factor a 1 out of the absolute value to make the coefficient of x equal to 1

factor a 2 out of the absolute value to make the coefficient of x equal to 1

find a, h and k for 

the horizontal shift depends on the value of h when
, the horizontal shift is described as:
- the graph is shifted to the left h units
- the graph is shifted to the right h units
the vertical shift depends on the value of k