The image of the graph is missing, so i have attached it.
Answer:
g(x) = 5/3 * f(x)
Explanation:
We want to find the equation represents g(x) as a translation of f(x).
From the graph, the y = f(x) function curve has the following observations,
- At x = 0, y = f(0) = 30
- At x = 10, y = f(10) = 36
Similarly, from the graph, the y = g(x) function curve has the following observations,
- At x = 0, y = g(0) = 50
- At x = 10, y = g(10) = 60
From those coordinates on the graph, we can see that;
f(0) = 30 and g(0) = 50
It means that for us to make g(x) as a translation of f(x), g(0) = fraction * f(0)
Fraction = g(0)/f(0) = 50/30 = 5/3
Thus;
g(x) = 5/3 * f(x)
Let's confirm with the second coordinate;
Thus;
g(10) = 5/3 * f(10)
g(10) = 5/3 * 36
g(10) = 60
This value is same as what is on graph, thus we can conclude that;
The equation represents g(x) as a translation of f(x) is; g(x) = 5/3 * f(x)