
bergauf
uphill
Describes movement or direction up a mountain or hill; upward on an incline.
Die letzte Etappe der Wanderung führte steil bergauf.
The last stage of the hike went steeply uphill.
uphill
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uphill
Describes movement or direction up a mountain or hill; upward on an incline.
Die letzte Etappe der Wanderung führte steil bergauf.
The last stage of the hike went steeply uphill.

to improve
To improve in a figurative sense or take a positive turn, for example economically or personally.
Nach ein paar schwierigen Monaten geht es für die Firma endlich wieder bergauf.
After a few difficult months, things are finally improving again for the company.
The word is made up of 'Berg' (mountain) and 'auf' (up/on). So it literally describes a movement 'up a mountain', which makes the meaning very clear.
Wir müssen noch etwa einen Kilometer bergauf gehen.
We still have to walk uphill for about one kilometer.
As an adverb, 'bergauf' (uphill) usually stands at the end of a sentence or clause and describes the direction of an action. But it can also stand alone as an answer to a 'Wohin?' (where to?) question.
Die Straße führt hier steil bergauf.
The road goes steeply uphill here.
You can almost always recognize the figurative meaning by the fixed expression 'es geht bergauf' (things are improving). The subject is 'es' or an abstract concept such as 'die Wirtschaft' (the economy) or 'meine Karriere' (my career).
Nach der Krise geht es mit der Wirtschaft langsam wieder bergauf.
After the crisis, the economy is slowly improving again.
In the literal meaning, 'bergauf' (uphill) is often combined with verbs of movement. Typical examples are 'bergauf gehen' (to walk uphill), 'bergauf fahren' (to drive/ride uphill), 'bergauf steigen' (to climb uphill), and 'bergauf radeln' (to cycle uphill).
Mit dem E-Bike kann man viel leichter bergauf fahren.
With an e-bike, you can ride uphill much more easily.
high
Hoch and bergauf can describe movement on an incline. Hoch usually appears together with the route mentioned, such as “den Berg hoch.” Bergauf describes the uphill direction itself and does not need such an addition.

Wir gehen auf dem steilen Weg langsam bergauf.
We are slowly walking uphill along the steep path.
Wir gehen den steilen Berg langsam hoch.
We are slowly walking up the steep mountain.