ANALYZE A PROBLEM Describe the x-values for which (a) f is increasing (b) f is decreasing, (c) f (x) > 0 and (d) f (x) < 0

Question

2 years ago

5

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1 answer:

Karolina [17] · Answer 1 · 2024-01-11T06:11:41+03:00

The analysis of the graph, that has x-intercepts of (0, 2), and (0, 5), we get;

a. The function increases when x > 4

b. The function decreases when x < 4

c. The function is greater than zero when x < 3, and x > 5

d. The function is less than zero when 3 < x < 5

<h3>What is a point where a function is increasing?</h3>

The location of a point where a function is increasing is where the slope of the function is larger than zero.

The description of the graph of the function are as follows;

The shape of the function = Concave upwards

The coordinates of the vertex of the function = (4, -5)

The region where the function is decreasing is from -∞ to 4

The region where the function is decreasing is therefore; x < 4

At the vertex, (4, -5), the slope of the function is zero, therefore;

Therefore, the function is increasing where x > 4

The x-intercepts are at point (0, 3) and (0, 5)

Therefore, the function is greater than zero when x < 3, and when x > 5

The function is less than zero in the range 3 < x < 5

Learn more about the graph of functions here:

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