Select the correct answer. Consider this absolute value function. f(x)= |x-5| How can function f be written as a piecewise funct
ion?
(multiple choice)
(multiple choice)
2 answers:
Answer:
Option A.
Step-by-step explanation:
An absolute value function can be written in two ways, as the absolute value sign does not allow negative values.
or
The only options with these equations are A. and D.
D. can be eliminated as the inequalities given for the piecewise function do not match f(x)
To see it visually, you can try graphing it on a calculator or internet graphing service.
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and 
. The x-terms cancel each other out giving us 
and y = -3. Now sub -3 into one of the equations to solve for x. x+2(-3)=-4, and x - 6 = -4. x = 2. So the solution for our system is (2, -3)
The solution to the equations are:
- 9x² - 36x + 36 = 0 has two equal real solutions
- x² - x + 4 = 0 has no real solutions
- The factored expression of 4x² + 23 – 35 is 4(x² -3)
The equation is given as:
The above equation is a quadratic equation which can be represented as:
The discriminant (d) is calculated as:
So, we have:
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
<h3>Part B: Describe the solution</h3>The equation is given as:
The above equation can be represented as:
The discriminant (d) is calculated as:
So, we have:
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
<h3>Part C: The solution to the expression</h3>We have:
Evaluate the difference
Factor out 4
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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