9514 1404 393
Answer:
- vertical shift: 7 (up)
- horizontal shift: 2 (right)
- vertical asymptote: x=2
- domain: x > 2
- range: all real numbers
Step-by-step explanation:
For any function f(x), the transformation f(x -h) +k represents a horizontal shift of h units to the right and k units upward.
Here, the parent function is log₂(x) and the transformation to log₂(x -2) +7 represents translation 2 units right and 7 units upward.
The parent function has a vertical asymptote at x=0, so the shifted function will have a vertical asymptote at x-2=0, or x = 2.
The parent function has a domain of x > 0, so the shifted function will have a domain of x-2 > 0, or x > 2.
The parent function has a range of "all real numbers." Shifting the function vertically does not change that range. The range of the shifted function is still "all real numbers."
The graph is shown below. The vertical asymptote is the dashed orange line.
_____
The "work" is in matching the pattern f(x -h) +k to the function log₂(x -2) +7.
So you can choose any number from 11 to 19.
I'll choose 11 for now.
Then you write, 11, the number, and then spell it out, eleven.
To show how many tens and ones, you can make a place value chart. You would make two boxes, the first one for tens and the other for ones.
You would put a 1 in the tens place and a 1 in the ones place.
I hope this helps!
Answer:
4√3
Step-by-step explanation:
5√27-2√48-5√3-(√3-2√3)2
= 5√(3x9)-2√(3x16)-5√3-2√3+4√3
= 5(3)√3-2(4)√3-5√3-2√3+4√3
= 15√3-8√3-5√3-2√3+4√3
= 4√3
Answer:
The answer is option D.
Step-by-step explanation:
You have to multiply it :
h(x) × g(x) = (h×g)(x)
(h×g)(x) = (x² + 2x)(-3x + 4)
(h×g)(x) = -3x³ + 4x² - 6x² + 8x
(h×g)(x) = -3x³ - 2x² + 8x
The length of side of triangle is 5 units and length of side of pentagon is 1.5 units.
<u>SOLUTION:</u>
Given, An equilateral triangle has sides of length 
units.
Then, perimeter of the triangle will be 
A regular pentagon (5 sides) has sides of 
units.
Then, perimeter of the pentagon will be 
We have to find the dimensions of each shape
. Now, the perimeter of the triangle is twice the perimeter of the pentagon,
So, 
Then, length of side of triangle 
Length of side of pentagon 
We have to neglect, negative sign as lengths can’t be negative. Even if we change the sign above all conditions are satisfied.
