Question

Can someone help? i cannot get this question right

Answer 1

Answer:

  see below

Step-by-step explanation:

The function f(x) is the absolute value function scaled vertically and shifted up. Neither of those transformations affects the interval on which it is increasing. The absolute value function increases for x > 0. (It is neither increasing nor decreasing at x=0.)

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The function g(x) is a parabola that opens downward. Consequently, it is increasing for all values of x to the left of its vertex (or line of symmetry). That line of symmetry can be found as ...

  x = -b/(2a) = -(8)/(2·(-1)) = 4

So g(x) is increasing from -∞ to 4, but at x=4 is neither increasing nor decreasing.

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Then the interval on which both functions are increasing is ...

  {x > 0} ∩ {x < 4} = {0 < x < 4}

This will be graphed as a line between 0 and 4 with open circles at each end.

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The second attachment shows the two functions so you can see where their slopes are positive.