Answer:
Step-by-step explanation:
We have the two functions:
And we want to find:
This is equivalent to:
Therefore, we will have:
By substitution:
Simplify. Square and distribute:
Rearrange:
Combine like terms:
"Undefined" slope means the line is vertical, of the form x = constant. The constant is the x-value of the point the line goes through.
C) x = 2
Answer:
(-4, 0) U (1, ∞)
Step-by-step explanation:
Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).
x = 0 x-1 = 0 x + 4 = 0
x = 1 x = -4
Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.
far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0 → (-)(-)(-) > 0 → negative > 0 FALSE
- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0 → (-)(-)(+) > 0 → positive > 0 TRUE
0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0 → (+)(-)(+) > 0 → negative > 0 FALSE
far right (I choose 2): 2(2 - 1)(2 + 4) > 0 → (+)(+)(+) > 0 → positive > 0 TRUE
