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
You might be interested in
<h2>Answer:</h2>
A. It is a many-to-one function.
<h2>Step-by-step explanation:</h2>Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:
When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:
<h3>A. It is a many-to-one function.</h3>True
A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line , and you can see from the first figure below that
is mapped onto
. so this is a many-to-one function.
Since this is a many-to-one function, it can't be a one-to-one function.
<h3>C. It is not a function.</h3>False
Indeed, this is a function
<h3>D. It fails the vertical line test.</h3>False
It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.