Given a function f(x) we translate the function:
• a units horizontally (a > 0 to the right, a < 0 to the left),
,• b units vertically (b > 0 up, b < 0 down),
by the transformation:
In this case, we have:
Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:
• a = 2 units to the right,
,• b = 4 units up.
Translating the graph of f(x), we get:
AnswerThe translated graph is the graph in red:
Answer:
8
Step-by-step explanation:
0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;
1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';
2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;
3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);
4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);
5) if t=3/(v-5) and t=13/(v+5), then