Question

A graph of a function of x is shown. What statement best describes the function? Choose four and show work.A. The function has a minimum.B. The function has a maximum.C. The function is increasing for x values from negative infinity to 6.D. The function is increasing for x values from 6 to infinity.E. The function is decreasing for x values from negative infinity to 6.F. The function is decreasing for x values from 6 to infinity.G. The function is linear. H. The function is nonlinear.

Answer 1

When we plot a linear function it looks like a line, which is not the case here, so the first thing that we can say is:

H. The function is not linear

When we look at the graph of the function, we can see that the function is decreasing from minus infinity to 6, then another statement that describes the functions is:

E. The function is decreasing for x values from negative infinity to 6.

We can also see that the function increases from 6 to infinity, then:

D. The function is increasing for x values from 6 to infinity.

And since at the x value of 6, the behaviour of the function is changing from a decrease to an increase, here we have a minimum point, and then:

A. The function has a minimum.