determine the intervals in which the graph is increasing

Question

Determine the intervals where the graph increases.

I don't know how to draw a graph here or if it is possible.

I think that the answer is B, but I'm not really sure.

Answer 1

The answer is $(C)$ because this sine curve is increasing from the minima at $(-1,-1)$ to the maxima at $(1,1)$

Answer 2

Hint:

The graph is increasing at a point $x$ if the function values of points smaller than $x$ are also smaller than $f(x)$, and function values of points larger than $x$ are larger than $f(x)$.

Looking at the graph, that means that for a given number $x$, you look at the point $P=(x,f(x))$ on the graph. The function is increasing if the points to the left of $P$ are below $P$ and points to the right of $P$ are above it.

Answer 3

The answer is C) $[-1,1]$. The function is said to be increasing if $x\geq y\implies f(x)\geq f(y)$. So for the portion between $x=-1$ and $x=1$ the function value is increasing as depicted on the graph.

Answer 4

We say that $f(x)$ is increasing in the interval $(a,b)$ , if for each $x_1,x_2\in (a,b)$ , $ x_2>x_1 \Rightarrow f(x_2)>f(x_1)$.

So the answer is $C$.

Answer 5

When students struggle with these types of questions, I often encourage them to imagine that the graph represents a rollercoaster that travels from left to right. (Take a look at the image that is attached.) enter image description here Notice that wherever the rollercoaster ride is increasing would be considered an increasing interval and wherever the ride is decreasing would be a decreasing interval. So, if you imagine that this graph represents a rollercoaster ride, it’s quite easy to see that the ride increases within the interval (-1,1). So the answer is C.