if you vertically shift the absolute value parent function, f(x)=lxl up five units what is the equation of the new function?
2 answers:
Answer:
Step-by-step explanation:
There is a parent function in absolute value as
f(x) = |x|
Given that this is shifted up by 5 units
This means no horizontal shift so x remains as it is
Since vertically shifted by 5 units, we get new function as
This will make the parent function shift by 5 units up and hence y intercept would be
f(0) = 5
This function would be having minimum at (0,5) and symmetrical about x=0
Domain = all real numbers
Range =[5,infty)
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The 24th term is 152
Step-by-step explanation:
The formula of the nth term of an arithmetic sequence is:
, where
- a is the first term
- d is the common difference between consecutive terms
The third term means n = 3
∵
∴
∵ = 5
- Equate the right hand sides of the third term
∴ a + 2d = 5 ⇒ (1)
The fifth term means n = 5
∵
∴
∵ = 19
- Equate the right hand sides of the fifth term
∴ a + 4d = 19 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from equation (2) to eliminate a
∴ 2d = 14
- Divide both sides by 2
∴ d = 7
- Substitute the value of d in equation (1) to find a
∵ a + 2(7) = 5
∴ a + 14 = 5
- Subtract 14 from both sides
∴ a = -9
The twenty fourth term means n = 24
∵ a = -9 and d = 7
- Substitute the values of a and d in the formula of the nth term
∴
∴
∴
∴
The 24th term is 152
Learn more:
You can learn more about the arithmetic sequence in brainly.com/question/7221312
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