Which of the  statements is true regarding the function‘s intervals of increase and decrease? a) The function is decreasing when x< 4 and increasing when x> 4 b) The function is always...

Which of the  statements is true regarding the function‘s intervals of increase and decrease?

a)

The function is decreasing when x< 4 and increasing when x> 4

b)

The function is always decreasing

c)

The function is always increasing

Asked on by foxwit

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1 Answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The image provided by the problem shows that the graph of the function intersects x axis at `x = 4` , hence, the equation of the function has a real solution at `x= 4` .

You may notice that the graph of the function goes down along a vertical line `x = 3` , parallel to y axis, hence, the graph of the function has a vertical asymptote `x = 3.`

You may notice that the the larger the x values are, the larger the y values are, hence, using the definition of increasing function `x_1<x_2 => y_1<y_2` , yields that the function is always increasing.

Hence, since the function is always increasing, you need to select the answer c).