Question

select all the intervals where f is decreasing. y = f(x) choose all answers that apply: a -5 < x < -2.5 b -2.5 < x < 1.75 c 1.75 < x < 5 d none of the above

Explanation:

Step1: Recall decreasing - function property

A function $y = f(x)$ is decreasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$. Graphically, the function is decreasing when the graph moves down - ward as we move from left to right.

Step2: Analyze the given graph

Looking at the graph of $y = f(x)$, we can see that the function is decreasing on the interval where the curve is sloping downwards. The function $y = f(x)$ is increasing on some intervals and decreasing on others. The function appears to be decreasing on the interval starting from approximately $x = 1.75$ and going to the right - hand side of the visible part of the graph. Since the right - hand end of the visible graph is around $x = 5$, the function is decreasing on the interval $1.75

Answer:

C. $1.75 < x < 5$