Question

1. Find g(x), where g(x) is the translation 7 units up of f(x) = x.

2. Find g(x), where g(x) is the translation 5 units left of f(x) = x2.


3. Find g(x), where g(x) is the translation 3 units right and 4 units up of f(x) = x2.


4. Find g(x), where g(x) is the translation 1 unit left and 5 units down of f(x) = |x|.

Answer 1

Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.

Step-by-step explanation:

To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.

1. Translation 7 units up of f(x) = x results in g(x) = x + 7.
2. For the translation 5 units left of f(x) = x2, we use g(x) = (x + 5)2.
3. The translation 3 units right and 4 units up of f(x) = x2 gives us g(x) = (x - 3)2 + 4.
4. Translation 1 unit left and 5 units down of f(x) = |x| leads to g(x) = |x + 1| - 5.

In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.