Question

Determine the interval (s) on which the given function is increasing

Answer 1

x in ] -∞ , 0 [ U ] 1 , ∞ [

The function is increasing for these values of x

Answer 2

Answer:

$\{ x: x < 0 \} \cup \{ x: x > 1 \}$

Step-by-step explanation:

A function is increasing when its gradient is positive (so y-coordinates are increasing).

We have a graph, rather than a function given to us, so we don't need to use any calculus.

Looking at the graph, we can see that before x=0, the graph is going up (gradient is increasing).

Between x=0 and x=1, the function is decreasing.

After x=1, the function is increasing again.

We can use mathematical notation to express this.

$\{ x: x < 0 \} \cup \{ x: x > 1 \}$

Or

$x < 0\ \text{and}\ x > 1$