The graph of y= - 1/2x+2 is positive over the interval (4, infinity) and negative over the interval (-infinity, 4) .What happens on the graph when x=4? explain

The graph of y=ax+b, where a≠0, is always a line:

i) increasing if a>0
ii) decreasing if a<0

Consider the decreasing case.

The line is above the x-axis, that is positive but decreasing. At 1 single point it cuts the x-axis, so x=0, and then it continues decreasing below the x-axis.

Back to our problem:

The graph of y=-1/2 x +2 is a decreasing line.,

so it CANNOT be
"positive over the interval (4, infinity) and negative over the interval (-infinity, 4)"

it is

"negative over the interval (4, infinity) and positive over the interval (-infinity, 4)"

the graph is "positive over the interval (-infinity, 4)", it means that the line is decreasing but above the x-axis until 4, (4 not included).

then, "negative over the interval (4, infinity)", which means that the line is now decreasing below the x-axis.

when x=4, the line cuts the x-axis.

check the graph of the line generated using desmos.com

facundo3141592 facundo3141592 · Answer 2 · 2021-09-04T15:21:06+02:00

This is a problem of linear functions, where we want to see what happens for a particular value, x = 4, which we will find is the x-intercept.

Here we have the function:

[tex]y = -(1/2)*x + 2[/tex]

Yo say that:

"it is positive over the interval (4, ∞) and negative over the interval (-∞,4)"

This is clearly wrong, for example, if we evaluate the function in x = 5 (in the positive interval) we get:

[tex]y = -(1/2)*5 + 2 = -2.5 + 2 = -0.5[/tex]

So the function is negative in x = 5.

Then it should say:

"It is positive over the interval (-∞,4) and negative over the interval (4, ∞)"

Now that this is explained, we want to see what happens on the graph when x = 4.

To see this, the first thing we can do is to evaluate the line in x = 4, we will get:

[tex]y = -(1/2)*4 + 2 = -2 + 2 = 0[/tex]

Having the y-component equal to zero means that the function intercepts the x-axis.

So from this, we can see that the x-intercept is the point (4, 0).

A graph of the function is shown below, where you can see this.

If you want to learn more, you can read:

https://brainly.com/question/11872755