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3 years ago

What is the vertex of the graph of g(x)=|x-9|+3

Mathematics

1 answer:

mart [117]3 years ago

7 0

Look at h(x) = |x-9|. The vertex of this absolute value function graph is at (9,0).

Sometimes it helps to work on a simpler problem first, which is why I've introduced h(x) = |x-9|.

The vertex of g(x)=|x-9|+3 is 0+3, or 3; we translate the entire graph of g(x)=|x-9| upward by 3 units. Thus, the vertex of g(x) is (9,3).

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2 years ago

Please help. Look at screenshot

Citrus2011 [14]

Answer:

Increasing:

x < 0

x > 2

Decreasing:

0 < x < 2

-1 < x < 2

x > 2

x < -1

Step-by-step explanation:

Function is increasing when it is going up as we go rightward

Function is decreasing when it is going down as we go rightward

We can see that as we move up (from negative infinity) until x = 0, the function is increasing. Also, as we go right from x = 2 towards positive infinity, the function is going up (increasing).

So,

Increasing:

x < 0

x > 2

The function is going down, or decreasing, at the in-between points of increasing, that is from 0 to 2, so that would be:

Decreasing:

0 < x < 2

When we want where the function is greater than 0, we basically want the intervals at which the function is ABOVE the x-axis [ f(x) > 0 ].

Looking at the graph, it is

from -1 to 2 (x axis)

and 2 to positive infinity

We can write:

-1 < x < 2

x > 2

Now we want when the function is less than 0, that is basically saying when the function is BELOW the x-axis.

This will be the other intervals than the ones we mentioned above in part (b).

Looking at the graph, we see that the graph is below the x-axis when it is less than -1, so we can write:

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3 years ago

Answer correctly for the brainliest answer

Dahasolnce [82]

Similar triangles so AC:BC=AE:DE

15+6=21 = AE

15:12.5=21:?

to get from 15 to 12.5 you divide by 15 and times by 12.5 so do this the to the other side

21/15=1.4

1.4 x 12.5=17.5

So DE=17.5

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2 years ago