The graph of the function f(x) = (x + 2)(x − 4) is shown.



Which describes all of the values for which the graph is negative and increasing?


all real values of x where x < −2

all real values of x where −2 < x < 4

all real values of x where 1 < x < 4

all real values of x where x < 0

Verified Answer :

bcalle

The function is negative below the zeros which would be from -2 to 4.
It would be increasing from the vertex to the zero,4.
So the answer would be 1 < x < 4

The values for which the graph is negative and increasing are all real values of x where 1 < x < 4.

Given

The graph of function;

\(\rm f(x) = (x + 2)(x - 4)\)

What is a graph?

A graph goes from being negative to positive (or the other way around) by passing through the x-axis. in other words when f(x) = 0.  

Then,

\(\rm f(x) = (x + 2)(x - 4)=0\\\\x+2 =0\ x=-2\\\\x-4=0\ x=4\)

For increasing and decreasing for anything other than a quadratic and linear function you need calculus.  

The function is negative below the zeros which would be from -2 to 4.

It would be increasing from the vertex to zero,4.

Hence, the values for which the graph is negative and increasing are all real values of x where 1 < x < 4.

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