Question

48:15

The function f(x) = (x - 4)(x - 2) is shown
What is the range of the function?
O
O
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1

Answer 1

all real numbers greater then or equal to -1

Explanation:

Answer 2

all numbers greater than or equal to -1

Explanation:

Let's find the vertex.

Since the function is in factored form, I'm going to find the zeros.

The average of the zeros will give me the x-coordinate of the vertex.

I can then find the y-coordinate of the vertex by using the equation

y=(x-4)(x-2).

Also the parabola is open up since the coefficient of x^2 is positive (or 1 in this case).

So the range has something to do with the y's. It is where the function exist for the y-values.

So the range for this one since the parabola is open up will be of the form

[y-coordinate of vertex , infinity).

So let's begin.

The zeros can found by solving (x-4)(x-2)=0.

This means we need to solve both x-4=0 and x-2=0.

x-4=0 gives us x=4

x-2=0 gives us x=2

Now the average of our x-intercepts (or zeros) is (4+2)/2=6/2=3.

So the x-coordinate of the vertex is 3. To find the y-coordinate of the vertex we are going to use y=(x-4)(x-2) where x=3.

Plug in: y=(3-4)(3-2)=(-1)(1)=-1.

So the range is
`[-1,\infty)`

or all numbers greater than or equal to -1