What is the range of the function? The function f(x) = -(x+5)(x+1) is shown.
2 answers:
Answer:
all real numbers less than or equal to 4
Step-by-step explanation:
To obtain the range we require the value of the y- coordinate of the vertex.
Given
f(x) = - (x + 5)(x + 1) ← equate f(x) to zero to find the zeros, that is
- (x + 5)(x + 1) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 1 = 0 ⇒ x = - 1
The vertex lies on the axis of symmetry which is at the midpoint of the zeros
=
=
= - 3
Substitute x = - 3 into f(x) for y- coordinate of vertex
= - (- 3 + 5)(- 3 + 1) = - (2)(- 2) = 4
The vertex = (- 3, 4 )
and - (x + 5)(x + 1) = - (x² + 6x + 5) = - x² - 6x - 5
Since the coefficient of the x² term is - 1 < 0
then the vertex is a maximum ∩
Hence range is [ 4, - ∞ )
That is all real numbers less than or equal to 4
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Answer:
Step-by-step explanation:
Given:
Type of Flowers = 5
To choose = 4
Required
Number of ways 4 can be chosen
The first flower can be chosen in 5 ways
The second flower can be chosen in 4 ways
The third flower can be chosen in 3 ways
The fourth flower can be chosen in 2 ways
Total Number of Selection = 5 * 4 * 3 * 2
Total Number of Selection = 120 ways;
Alternatively, this can be solved using concept of Permutation;
Given that 4 flowers to be chosen from 5,
then n = 5 and r = 4
Such that
Substitute 5 for n and 4 for r
Hence, the number of ways the florist can chose 4 flowers from 5 is 120 ways